4 Tan A/1-Tan^4=Tan2A + Sin2A​

Answers

Answer 1

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)


Related Questions

help me find m and b

Answers

Answer:

m = 2/3

b = -1

y = 2/3x - 1

Step-by-step explanation:

Answer:

y=2/3x-1

Step-by-step explanation:

. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it
take him to fill the bottle?

Answers

Answer:

1/2 minute

Step-by-step explanation:

We can use a ratio to solve

1/3 bottle     1 bottle

------------   = --------------

1/6 minute    x minutes

Using cross products

1/3x = 1/6 *1

1/3 x = 1/6

Multiply each side by 3

3 * 1/3x = 3 * 1/6

x = 3/6

x = 1/2

1/2 minute

Answer:

30 seconds (1/2 minute)

Step-by-step explanation:

We are given that,

Amount of water filled in 1/6 minute = 1/3

Now, Let the time taken to fill the whole bottle with water be x

Hence,

Through the ratio method we get,

1/3:1/6 : : 1:x

Hence, we need to multiply the extremes and the means together and equalize them.

Hence,

x/3=1/6

x=(1/6)×3

x=(1/2) minute or 30 seconds

Question 3 (2 points)
Use the figure below to answer the following questions. Find the measure of each angle.

Answers

Answer:

∠ 1 = 70°, ∠ 2 = 140

Step-by-step explanation:

110° and the adjacent angle inside the triangle are supplementary, then

angle = 180° - 110° = 70°

Since 2 sides of the triangle are congruent, then the triangle is isosceles

Thus the 2 base angles are congruent, then

∠ 1 = 70°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 2 is an exterior angle of the triangle, thus

∠ 2 = 70° + 70° = 140°

integral 1-rootx/x dx​

Answers

r-1 over 2 |d| to2 r2 x3 +C

picture above
give the right answer and i’ll literally give 75 extra points and brainliest x2 , please help i can’t fail

Answers

Answer:

False :)

Step-by-step explanation:

Answer:

Not a function, therefore false.

Step-by-step explanation:

Maybe this attachment can help.

You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−6x+330, where x is the time (in seconds) since you first noticed the hot air balloon. ANSWER FASTTTTT!!!

Answers

Answer:

55 secs

Step-by-step explanation:

Given the elevation h (in feet) of the balloon modeled by the function h(x)=−6x+330, we can calculate the time it takes the balloon to reach the ground. The hot air balloon hits the ground at h(x) = 0.

Substitute h(x) = 0 into the modeled expression and find x as shown;

h(x)=−6x+330

0 = −6x+330

6x = 330

Divide both sides by 6

6x/6 = 330/6

x = 55 seconds

Hence the hot air balloon hits the ground after 55 seconds

Rosalina is driving to visit her family which live 150 km away her average speed is 60 km/h the cars tank is 20 L of fuel at the beginning of the drive and its fuel efficiency is 6 km perL fuel cost $.60 per liter how long can Roselene drive before she runs out of fuel

Answers

Answer:

With the amount of fuel she has, she can drive 120 km which will take 2 hours.

Step-by-step explanation:

You need to figure out which information is necessary for this problem and which is not.

The fuel tank has 20 L.

The car drives 6 km per L.

20 L * 6 km/L = 120 km

She can drive 120 km with the amount of fuel she has.

She is driving at 60 km/h.

speed = distance/time

time * speed = distance

time = distance/speed

time = (120 km)/(60 km/h) = 2 hours

Answer: With the amount of fuel she has, she can drive 120 km which will take 2 hours.

A woman sold a typewriter for Rs 13718 in the system of compound depriciation at the rate of 5 percent .If she had purchased it 3 years before how much did she pay for it by that time?

Answers

Answer:

Rs 16000

Step-by-step explanation:

Given that :

Price at which typewriter was sold = Rs 13718

Compound Depreciation rate = 5%

Time = 3 years

Amount paid for typewriter 3 years ago

Using the relation :

Final amount = Initial amount(1 - r/n)^nt

n = number of compounding times per period

Rate = r = 5% = 0.05

t = time

A = Final amount = 13718

Initial amount = original purchase price (p)

Therefore ;

13718 = p(1 - 0.05)^3

13718 = p(0.95)^3

13718 = p * 0.857375

13718 = 0.857375p

p = 13718 / 0.857375

P = Rs 16000

Amount paid at the time of purchase = 16000

What is the greatest cornron foctor (Gc) of 15 and 64?

Answers

The GCF of 15 and 64 is 1.

Mikhail has $4.15. If he buys one pack of candy canes, how much money does he have left? (the candy canes are $2.45 FOR A PACK OF 4 candy canes)

Answers

Answer:

1.70$

Step-by-step explanation:

$4.15-$2.45

=1.70$

Answer:

$1.70

Step-by-step explanation:

If you subtract the price of one pack of candy canes from how much money he has you get $1.70

(hope this helps)

A color printer prints 21 pages in 9 minutes. How many pages does it print per minute? Round your answer to the nearest hundredth.
? = pages per minute

Answers

Answer:

2.33 = x

Step-by-step explanation:

pages minutes

21 9

x 1

Cross multiply.

21×1 = 9×x

21 9x

9 9

9 cancels 9 leaving x. and 21 divided by 9 equals 2.33 pages. NB. both sides are divided by 9 because we want x by itself and what you do to one side, you have to do to the other.

The height of a room is 10 feet. You are installing floor-to-ceiling shelving, and each shelf is 8 inches tall. Write and solve an inequality for the number of shelves you could possibly build.

Answers

10 feet = 120 inches

120 divided by 8 = 15

you can have 15 shelves in the room

10ft=120
120 divided by 8=15

What will be the distance from the center of dilation, P, to the image S'?

2 units
4 units
6 units
8 units

Answers

Answer:

the answer is 6 units..

Find the value of x.

Answers

Answer:

x = 78

Step-by-step explanation:

180 - 60 - 42 = 78

Pardon me if i'm wrong :/

You would use Pythagorean theorem to solve. A+B=C

PLZ do all of it plz i will give brainlest and thanks to best answer

Answers

Answer:

1. -4

2. 10

3. -19

4. 5

Step-by-step explanation:

1. 5 + -9= -4

2. -3 + 13 = 10

3. -8 + 11 = -19

4. 6 + -1 = 5

20 POINTS and BRAINLIEST
Solve the simultaneous equation!

Answers

Answer:

x=7 y=-2

Step-by-step explanation:

The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.

Answers

Given :

The diagonals of rhombus ABCD intersect at E.

∠CAD = 20°.

To Find :

The angle ∠CDA.

Solution :

We know, diagonals of a rhombus bisects each other perpendicularly.

So, ∠DEA = 90°.

In triangle ΔEAD :

∠EAD + ∠AED + ∠EDA = 180°

20° + 90° + ∠EDA = 180°

∠EDA = 70°

Now, we know diagonal of rhombus also bisect the angle between two sides .

So, ∠CDA = 2∠EDA

∠CDA = 2×70°

∠CDA =140°

Therefore, ∠CDA is 140°.

what fraction is 3/4 equivalent to?

Answers

Answer:

6/8

Step-by-step explanation:

double both of them lol

Answer:

3/4 is equivalent to 6/8 and 12/16

Step-by-step explanation:

please help me !!!!!!!!!!!!!!!!

Answers

5Step-by-step explanation:

sin 40 cos 50 + cos 40 sin 50 find the value​

Answers

Answer:

= 1

Step-by-step explanation:

0.4131 + 0.5868 = 0.999 --> 1

Please help me out!!!!!

Answers

Answer:

To find a degree 3 equation you must find and take the roots.You have the roots at x=0 Now plug those into the equation for example: (x-4) would result in x1=4Hope this helps!

50 points!!! If your good at math please help! :) will give brainlest
Y is directly related to X, and Y is 81 when X is 27.

The constant of variation is ___
(there are no answer choices, it's just a type in box so i need an exact answer please! :))

Answers

Answer:

y=3x or x=y/3

Step-by-step explanation:

81, y divided by 3 is equal to 27.

Please help me, TYSM !!❣

Answers

Answer:

A

Step-by-step explanation:

thats my best guess, but im not positive sorry if im wrong!

The scores on a test are normally distrubuted with a mean of 60 and a standard deviation of 12. What is the score that is 2 1/2 standard deviations above the mean?

Answers

Answer:

?

Step-by-step explanation:

Find the measure of the indicated angle. Round to the nearest tenth of a
degree.

Answers

Step-by-step explanation:

Using trignometry, we have cosθ = Adjacent / Hypotenuse = 3/5.

Hence θ = cos-1(3/5) = 53.1° (A).

If the temperature outside increases by 3 1/2 degrees every 1 1/2 hours, by how much will the temperature increase after 4 hours?

please answer in fractions.

Part 1:

What is the rate per hour of the temperature increase?

Part 2:

How much will the temperature increase after 4 hours?

Answers

Answer:

Part 1:    7/3 degrees/hour

Part 2:    28/3 degrees

Step-by-step explanation:

Part 1:

3 1/2 degrees per 1 1/2 hours =

= (3 1/2)/(1 1/2)

= (7/2) / (3/2)

= 7/2 * 2/3

= 7/3 degrees/hour

The rate is 7/3 degree per hour

Part 2:

In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.

4 hours * 7/3 degree/hour = 28/3 degrees

The yellow turtle country covered 33 cm in six minutes her speed as a unit rate is blank a country walk blank in one minute

Answers

Answer:

5.5 cm/minute

Step-by-step explanation:

Given that,

The yellow turtle country covered 33 cm in six minutes.

To find unit rate, divide distance covered by the time.

Here, distance = 33 cm

Time, t = 6 minutes

[tex]R=\dfrac{33\ \text{cm}}{6\ \text{minutes}}\\\\=5.5\ \text{cm/minutes}[/tex]

Hence, the unit rate is 5.5 cm/minute. It means, Courtney covered 5.5 cm in one minute.

Answer I will mark branliest

Answers

Answer:

D 50

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

5y^2+4x

5(3)^2+4(2.5)

5(9)+4(2.5)

45+4(2.5)

45+10

=55

three fourths times two thirds .
a
five twelfths

b
six twelfths

c
five sevenths

d
six sevenths

Answers

Answer: 1/2

Step-by-step explanation: 3/4x2/3= 6/12=3/6=1/2. Hope this helps! Have a wonderful day/night! PLz mark me as brainliest!

Answer:

b) six twelfths

Step-by-step explanation:

(3/4)*(2/3) = 0.50.5 = 1/2 = 6/12 = six twelfths

A pair of designer blue jeans is on sale for $51. This is 75% of the original price. What was the original price of the jeans?

Answers

22 hope this helps have a nice day
Other Questions
From top to bottom, what is the correct order of the social structure of ancient Egypt?Pharaoh, Scribes, Priests, Merchants, FarmersPharaoh, Priests, Scribes, Merchants, Farmers plz help me this is due and thank you1. Jordan loves creating short films using his phone camera and small posable figures. He has learned how to edit the videos so that it looks as if the figures are alive and moving! What possible career paths might Jordan want to consider for his future? Explain.2. What important services do journalists and broadcasters perform for our community? Give one example of a situation where journalists or broadcasters are helpful.3. What quality might be important for someone who works in the Performing Arts pathway of the Arts, A/V Technology, and Communication career cluster? List three specific careers in that pathway and explain how the quality you chose would be important to have in order to succeed in each career.4. Josh began his career as the front desk clerk of a large hotel. He enjoys working in the Lodging pathway of the Hospitality and Tourism career cluster and plans to take more classes in hospitality and business. After finishing his education, what positions might be available to Josh along his career path?5. Kylie lives near a beautiful beach and has grown up surfing the waves. Many families come to visit her area and Kylie has noticed that visiting children are rarely successful when they try to surf. Taking advantage of her location and experience, what kind of service in the Hospitality and Tourism career cluster might Kylie think of offering, and why? All of the points in the picture are on the same line Describe how to find the inverse of the function.To find the inverse of the function, change f(x) to y, switch and y, and solve for . The resulting function can be written as , where . A rectangular lawn measures 6m by 10m. Angela is planning a mulch walkway of width "x" around the entire edge of the lawn. Write a function that represents the area of the lawn combined with the area of the walkway. How do you pay for stuff and what do you pay for? (What is the basis for your economy?) (Bartering & trade, coins/commerce, taxes, free market, command, etc.) Enter the coordinates of the pointon the unit circle at the given angle.45 [?]22 How original were Newtons contributions to science? (In what ways did Newton depend on the mechanical view?) Question 6In which of the following lists of mixed economies does the free market system dominate?CubaGreece, China, United StatesNorth Korea, France, South AfricaUnited States United Kingdom, Singapore, CanadaRussia, Peru, France, Canada Techniques used to rank individuals according to social class are a. reputational. c. objective. b. subjective. d. all of the above Please select the best answer from the choices provided A B C D Question 2 (1 point) These allow electricity to flow easily through them (think copper and aluminum). (Lessons 5.01-5.03) Electric Currents Resistors Conductors Insulators Which of the tables represents a function?Table AInput Output5 35 24 1Table BInput Output1 23 25 3Table CInput Output0 01 21 3Table DInput Output4 24 34 4(5 points)Table ATable BTable C neon, a monatomic gas, that starts out at conditions of standard temperature and pressure (273.15 K, 105 Pa). Alice heats the gas at constant volume until its pressure is doubled, then Bob further heats the gas at constant pressure until its volume is doubled. If Alice and Bob assume that neon behaves as an ideal gas, then how much heat have they added to the gas for the entire process. Decide whether the meaning is correct or incorrect as written.nosotros = wecorrectincorrect On average, Americans have lived in 4 places by the time they are 18 years old. Is this average a different number for college students? The 50 randomly selected college students who answered the survey question had lived in an average of 3.79 places by the time they were 18 years old. The standard deviation for the survey group was 1.2. What can be concluded at the = 0.10 level of significance? substitute =3in the following equation to find y5y - 2x=9 What did the Inca believe about their rulers?they could turn common elements into goldthey were descended from the Maya in Mesoamericathey were descended from the gods and never truly diedthey could not be defeated in battle with their enemies Which of the following verbs has an irregular yo form?A. ComerB. ConducirC. VivirD. Hablar Which of the following is an extended definition of shenanigans? Which statement best completes the diagram? Cause Effect ? Hinduism becomes India's main religion. O A. Indian people start worshipping only one god. OB. The Harappan civilization spreads across India. O c. Aryan people arrive in the Indus River valley. O D. The caste system in India is destroyed.