Please simplify the following trigonometric identity.

[tex]\displaystyle\frac{1}{\sec\alpha-\tan\alpha}[/tex]

Answers

Answer 1

Examining the question:

We are given the expression:

[tex]\frac{1}{Sec(\alpha)-Tan(\alpha)}[/tex]

We know from Basic trigonometry that:

[tex]Sec(\alpha) = \frac{1}{Cos(\alpha)}[/tex]

[tex]Tan(\alpha) = \frac{Sin(\alpha)}{Cos(\alpha)}[/tex]

Simplifying the expression:

Replacing these values in the given expression, we get:

[tex]\frac{1}{\frac{1}{Cos(\alpha)} -\frac{Sin(\alpha)}{Cos(\alpha)} }[/tex]

Since the denominator of both the values in the denominator is the same:

[tex]\frac{1}{\frac{1-Sin(\alpha)}{Cos(\alpha)} }[/tex]

We know that [tex]\frac{1}{\frac{a}{b} }[/tex] = [tex]\frac{b}{a}[/tex], using the same property:

[tex]\frac{Cos(\alpha)}{1-Sin(\alpha)}[/tex]

and we are done!

Answer 2

Answer:

cos a

---------------------

1  -sin (a)

Step-by-step explanation:

We know that sec a = 1/ cos (a)  and tan a = sin (a) / cos (a)

1

---------------------

1/ cos (a)  -sin (a) / cos (a)

Multiply the top and bottom by cos (a)

1* cos a

---------------------

( 1/ cos (a)  -sin (a) / cos (a)) * cos a

cos a

---------------------

1  -sin (a)


Related Questions

For each value of u , determine whether it is a solution to 23=4u-1 .

Answers

Answer:

6

Step-by-step explanation:

Transposition

23+1=4u

24=4u

Divide both side by 4

u=6

algebra 2

Can you help me pls

Answers

Answer:

ln25 = 3.219

ln50 = 3.912

ln22.3 = 3.105

lne^3 = 3lne = 3

ln0.45 = -0.799

Step-by-step explanation:

Calculator

Calculate the value of the expression. 4+2 (17 – 12) ​

Answers

Answer:

14

Step-by-step explanation:

4+34-24 (distribute)

Need some help with geometry not very good at it.


Can I have some help please?

Answers

Answer:

your answer will be A. 12/24

Step-by-step explanation:

XZ=12+12=24

COSX=12/24

hope this helps you...

Which statement best describes the point (2,-5)
A.5 units to the left and 2 units up from the origin
B. 5 units to the right and 2 units up from the origin
C. 2 units from the left and 5 units down from the origin
D. 2 units to the right and 5 units down from the origin
HELPPPPPP!!!!!!!

Answers

I believe your answer would be C. Hope this helped!

I WILL GIVE BRAINLIEST
And more points please answer

Answers

Answer:

Step-by-step explanation:

Answer: Linda's 1/2 .  Phil's $0.50

Step-by-step explanation: the rate is the slop which is rise/run if that makes sense

Select the correct answer from each drop-down menu.
A cylinder has a diameter of 10 units.
Its radius is
units. If its height is twice its radius, its height is
units. Its volume is about
cubic units

Answers

Radius = 5 units
Height = 10 units
Volume = 785.4 units

Answer:

1st blank: 5

2nd blank: 10

3rd blank: 785

Step-by-step explanation:

the radius of a circle or the base/top of a cylinder is measured from the center to the side of the face, where as the diameter is measured from side to side through the middle, so the diameter will always be twice the radius of the same circle, meaning if the diameter is 10 units, then the radius will be half that, 5 units, then all we do is double the radius like the question says to get the height (NOTE this is NOT part of any formula for finding any dimensions for any shape and is specific to this question) then all we do to find the volume is use the formula below

V = (pi) (r^2) h

plug the radius or 'r' in as well as height or 'h' in the equation and solve

PLEASE NOTE: the question is asking for an APROXAMATE so your answer should be close to one of the drop down options by about >1 integer, but will not be exact

How are the acute angles of the right triangle below related? Please don’t answer me with a link

Answers

Answer:

An acute angle is an angle whose measure is less than 90∘. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are acute. A right angle is an angle whose measure is equal to 90∘. That is the measure of the angles of perpendicular lines.

Step-by-step explanation:

9. A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.9, and the probability that it is received incorrectly (as a 1) is 0.1. When a 1 is sent, the probability that it is received correctly is 0.8, and the probability that it is received incorrectly (as a 0) is 0.2. (a) Find the probability that a 0 is received. (b) Use Bayes theorem to find the probability that a 0 was transmitted, given that a 0 was received.

Answers

Answer:

a) 0.6667 = 66.67% probability that a 0 is received.

b) 0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

(a) Find the probability that a 0 is received.

0.9 of 2/3(0 received when a 0 is sent).

0.2 of 1/3(0 received when a 1 is sent). So

[tex]p = \frac{0.9*2}{3} + \frac{0.2*1}{3} = 0.6667[/tex]

0.6667 = 66.67% probability that a 0 is received.

(b) Use Bayes theorem to find the probability that a 0 was transmitted, given that a 0 was received.

Event A: 0 received

Event B: 0 transmitted.

0.6667 = 66.67% probability that a 0 is received, which means that [tex]P(A) = 0.6667[/tex]

A zero is transmitted two-thirds of time, which means that [tex]P(B) = 0.6667[/tex]

When a 0 is sent, the probability that it is received correctly is 0.9, which means that [tex]P(B|A) = 0.9[/tex]

So

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.6667*0.9}{0.6667} = 0.9[/tex]

0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.

I’m pretty sure the answer is a ?

Answers

I believe that it’s B

this dot plot is symmetric, and the data set has no extreme values

Answers

Answer:

Where is the plot?

Step-by-step explanation:

Select all the statements that are true

Answers

Answer:

Options 2, 4 and 6 are True.

Step-by-step explanation:

Triangle MNO is dilated by a scale factor of [tex]\frac{3}{2}[/tex] centered at M(0, 6).

Rule to be followed to dilate the vertices of the given triangle,

(x, y) → (kx, ky)

Here, k = scale factor

By this rule vertices of the new triangle M'N'O' will be,

M(0, 6) → M'(0, 6) [Coordinates of M' will remain same as M because center of dilation is point M]

N(-4, -4) → N'(-6, -6)

O(6, -2) → O'(9, -3)

Option 1

M'N' is shorter than MN

Distance between M and N = [tex]\sqrt{(0+4)^2+(6+4)^2}[/tex]

                                              = 10.77

Distance between M' and N' = [tex]\sqrt{(0+6)^2+(6+6)^2}[/tex]

                                                = 13.42

Therefore M'N' > MN

Therefore, Option A is False.

Option 2

ON is shorter than O'N'

True.

Option 3

OM is longer than O'M'

False

Option 4

ON is parallel to O'N'

Since OM and MN are dilated with the same scale factor, O'N' will be parallel to ON.

True.

Option 5

OM is parallel than O'M'

Since, O'M' is the dilated form of OM,

Therefore, all the points (O, M and M') will be in a straight line.

False

Option 6

M'N' coincide with MN

True.

Therefore, Options 2, 4 and 6 are True.

Can someone please help i would really appreciate it

Answers

Answer:

[0, -7, 1]

[0, 3, 4]

please help this is due today

Answers

Answer:

A and D

Step-by-step explanation:

A) x = 3

B) x = 0

C) x = ⅓

D = x = 3

Answer:

A and D

Step-by-step explanation:

Round 8 5/9 to the nearest whole number. 9 10 7 8

Answers

Answer:

The answer would be 9,

Step-by-step explanation:

because it is closer to 9 than 8.

PLEASE PLEASE HELP!! A ferris wheel with a radius of 38 feet rotates at a rate of 8 revolutions per minute. The height above the ground of the carriage labeled C below is a function of time, t, in minutes

Answers

Is this the whole question

Plz help me! Plz it’s due today,!

Answers

Answer: I think it is D

Step-by-step explanation:

in volume you multiply all the numbers(LxWxH)

hope this helps

It’s the last answer, 9(8)(1) = 72 cm^3

How many solutions does the system of equations have?

a. no solution
b. one solution x=0, y=5
c. One solution x=1, y=4
d. Infinitely many solutions

Answers

Answer:

one solution at x=1,y=4 point

Answer is =c due to the one solution

Cart 1 (500 g) moves to the right at 0.40 m/s. Cart 2 (250g) moves to the left at 0.50 m/s. a. If the carts stick after the collision, what will be their velocity?

Answers

Answer:

after the collision cart 1 will stop and cart 2 will keep moving will 0.1.m/s after stop.

If Tyesha only wants to eat 115 calories of the Italian Ice, how many ounces is she allowed to eat?

Answers

Answer:

Answered!!

Step-by-step explanation:

If Tyesha only wants to eat 115 calories of the Italian Ice, how many ounces is she allowed to eat? In this case she is only allowed to eat 10 ounces

This graph is the parent function of quadratic functions
True or false

Answers

true the graph is the parent function of quadratic functions

okok so this isnt a question but as i was scrolling through brainly and suddenly the lights went off and everybody was in the living room, the door was closed and it wasnt a electricity problem somrwiefnau help im nervous i don know what to do

Answers

Oh for real ? That’s scary

someone please help me answer this!!

Answers

Answer:

0.55x10= 5.50

Step-by-step explanation:

A group of volunteers has been collecting toys to deliver to a local charity. Over the last 3 days, the volunteers have collected 324 toys. What has been their collection rate, in toys per day?
A.
110 toys per day
B.
105 toys per day
C.
107 toys per day
D.
108 toys per day

Answers

Answer:

D 108

Step-by-step explanation:

324/3=108

Answer: 108 toys per day

Step-by-step explanation: 324/3

The table shows the cost of hiring a concrete mixer for up to 5 days.
1
2
Number of days
3
4
5
19
45
Cost in £
32
58 71
The cost of hiring the concrete mixer is made up
of a fixed charge and a daily charge.
(1)
(i) How much is the daily charge? £
(1)
(ii) How much is the fixed charge? £
Tota​

Answers

Answer:

i. daily charge = £13

ii. fixed charge = £6

Step-by-step explanation:

Number of days (x) | Cost in £ (y)

1 | 19

2 | 32

3 | 45

4 | 58

5 | 71

Using the given table, we can represent this situation with an equation in slope-intercept form, y = mx + b, where,

m = slope = daily charge

b = y-intercept = fixed charge

✔️Thus, using the coordinates of any two given pairs, say (1, 19) and (2, 32):

Slope (m) = ∆y/∆x = (32 - 19)/(2 - 1) = 13/1

Slope (m) = 13

Therefore daily charge = £13

✔️To find y-intercept (b), substitute (x, y) = (1, 19) and m = 13 into y = mx + b.

Thus:

19 = (13)(1) + b

19 = 13 + b

b = 19 - 13

b = 6

Therefore, fixed charge = £6

✔️Substitute m = 13 and b = 6 into y = mx + b to represent the function given for the situation:

y = 13x + 6

Please help me quick​

Answers

Answer: 20 inches

Step-by-step explanation:

using pythagorean theorem according to which  hypotebous ^2=altitude ^2+base^2

c^2=a^2+b^2

c^=(12)^2+(16)^2

c^2=144+256

c^2=400

c=20

Games at the carnival cost $3 each. The prizes awarded to winner cost $145.65. How many games must be played to make at least $50?

Answers

Answer:About 17 games

Step-by-step explanation:

$50 divided by $3 is about 17 games

the square root of 125 is closest to what whole number? *

Answers

Answer:

11

Step-by-step explanation:

the square root of 125 is 11.18033989 so when you round it you get 11

Please help! Answer and explanation please!

Answers

Answer:

12

Step-by-step explanation:

Since we can infer that those lines are the same length...

5x-15 = 3x+9

2x -15 = 9

2x = 24

x = 12

Which graph could represent a function f(x) = log(x + b) where b < 0?

Answers

Answer:

I think that the answer would be B .

Hope it helps . ♡

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