how do you simplify
[tex] \frac{ \sin(90 - \alpha ) \times \tan( - \alpha ) \times \cos( \alpha - 180) }{ \ \cos(100) \sin(135?) } [/tex]

Answers

Answer 1

Answer:

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]

Explanation:

The given expression is presented as follows;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})}[/tex]

The sine, cosine, and tangent of the common angles are given as follows;

sin(A - B) = sin(A)·cos(B) - cos(A)·sin(B)

∴ sin(90° - α) = sin(90°)·cos(α) - cos(90°)·sin(α) = cos(α)

tan(-α) = -tan(α)

cos(A - B) = cos(A)·cos(B) + sin(A)·sin(B)

∴ cos(α - 180°) = cos(α)·cos(180°) + sin(α)·sin(180°) = -cos(α)

sin(135°) = sin(90° + 45°) = sin(90°)·cos(45°) + sin(45°)·cos(90°) = cos(45°) = √2/2

Therefore, we get;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times -cos( 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{cos( \alpha) \times -tan (\alpha) \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}}[/tex]

[tex]\dfrac{cos( \alpha) \times -\dfrac{sin(\alpha)}{cos(\alpha)} \times -cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) \times \dfrac{\sqrt{2} }{2}} = \dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) }[/tex]

[tex]\dfrac{2}{\sqrt{2} } \times \dfrac{sin( \alpha) \times cos(\alpha )}{cos(100^{\circ}) } = \dfrac{sin(2 \times \alpha) }{\sqrt{2} \times cos(100^{\circ}) }[/tex]

Therefore;

[tex]\dfrac{sin(90^{\circ} - \alpha) \times tan (-\alpha) \times cos(\alpha - 180^{\circ})}{cos(100^{\circ}) \times sin(135 ^{\circ})} = \dfrac{\sqrt{2} \times sin(2 \times \alpha) }{2 \times cos(100^{\circ}) }[/tex]


Related Questions

>What is the output of the following code:

list1 = [ 'cyber', 786 , 2.23, 'square', 70.2 ]
print (list1[1] )

Answers

Answer:

Given code output is "786".

Explanation:

Code:

list1 = [ 'cyber', 786 , 2.23, 'square', 70.2 ]#defining a list list1 that holds value in parameter

print (list1[1] )#use a print method that prints list index value

In the given code a list "list1" is declared that holds value in it and in the next step a print method is declared that prints the first index value of the list.

pls any one what is pheumatic and hydrautic ​

Answers

Answer:

pheumatic is a branch of engineering that make use of gas

hydraulic is a technology and aplied science using engineering

Investigate the many ways that hardware and software can cause an interrupt to occur. Are ALL interrupts treated equally or do some have priority over others?​

Answers

Answer:

Following are the responses to the given question:  

Explanation:

This list is based mostly on the processor. Then you'll be ordered. An interrupt of a particular cable (wire) is produced for PC-ish CPUs (IRQ 0 - 31 for some intel processors). The bigger challenge is a lower number.

Strange factors have included a system clock, power business, 0, some reserved for use by CPU testing, serial/parallel/... ports and also some terminated/error/state/new devices requests device Thus a key touch on the keyboards could create an interrupt that was direct on old devices.

Two use of dovetail saw

Answers

Answer:

They are particularly use when it is use for cutting small or very precise cut. They are particularly use in joint making mostly dovetail joints

hope it helps

Tin học đã làm thay đổi công tác văn phòng ngày nay như thế nào?

Answers

Công nghệ đã thay đổi cách mọi người sử dụng để giao tiếp ở nơi làm việc hiện đại

Use the ________ predefined formats to quickly format cells.

Style Formats
Cell Styles
Cell Definitions
Cell Formats

Answers

Cell formats because I took it aboit 5 times and that was the answer so yeah

Answer:

I think choose (2)

Cell styles

True or False: Microsoft Publisher allows you to click and drag an element anywhere on the page.

Answers

Answer:

True

Explanation:

What is a benefit of using a client/server network?
Cheap to maintain
Easy to install
Has a central, powerful computer
Unable to share files

Answers

Answer:

Has a central powerful computer

Explanation:

When operating a client - server network, a certain access mediun is created such that clients can access information, materials and services from a central computer, this poses great advantage in the area of security and control. Clients would be able to gain access from this central computer using either a local or wide area network. The accessibility provided through this powerful, central computer allows the the network to monitor what actions are being performed and make appropriate restrictions on the network, hence, preventing the invasion of malware and viruses. Hence, the central control is a great feature of a client - server network.

write a program to enter RADIUS of a CIRCLE and PRINT AREA of TRIANGLE using Q Basic. (class 8)​

Answers

Answer:

The program is as follows:

10 INPUT RADIUS, BASE, HEIGHT

20 CIRCLE = 3.142* RADIUS * RADIUS

30 TRIANGLE = 0.5* BASE * HEIGHT

40 PRINT CIRCLE

50 PRINT TRIANGLE

60 STOP

Explanation:

The program description doesn't tally;

In other words, it is impossible to calculate the area of a triangle using the radius of a circle.

So, I designed the program to get input for radius, base and height.

Get input for radius, base and height

10 INPUT RADIUS, BASE, HEIGHT

Calculate area of circle

20 CIRCLE = 3.142* RADIUS * RADIUS

Calculate area of triangle

30 TRIANGLE = 0.5* BASE * HEIGHT

Print area of circle

40 PRINT CIRCLE

Print area of triangle

50 PRINT TRIANGLE

End of program

60 STOP

A current divider is to be designed using a 2mA DC current source and 1K resistors, the specification that the current is 1.5mA.

Answers

Answer:

The solution of the given query is described below throughout the explanation segment.

Explanation:

Given:

DC current,

= 2mA

Resistors,

= 1K

According to the question,

⇒ [tex]i=\frac{(1K+1K+1K)\times 2mA}{1K+1K+1K+1K}[/tex]

⇒   [tex]= \frac{3}{4}\times2mA[/tex]

⇒   [tex]=1.5mA[/tex]  

What is Adobe Dreamweaver ? What is it used for ? Name and describe its major components and features in detail​

Answers

Answer:

Part A

Adobe Dreamweaver is a computer application used for building websites and other types of web development, as well as mobile content development for both the intranet and the internet, on the Apple OS X and Windows Operating System Platforms

Part B

Adobe Dreamweaver is used for designing, building, and coding websites and mobile contents by developers and designers and by mobile content developers

Part C

i) Adobe Dreamweaver allows rapid flexible development of websites

The simplified engine on which Adobe Dreamweaver is based makes it easy to adapt web standards including CSS, and HTML for personalized web projects, thereby aiding learning of the web standards and fast (timely) web development

ii) The time between starting development and deployment is shorter when using Adobe Dreamweaver due to the availability of customizable templates that serve wide range of user web interfaces, including e-commerce pages, newsletters, emails and blogs

iii) Building of websites that adapts to the screen size of the device from where the site is accessed is possible with Adobe Dreamweaver

Explanation:

Complete the sentence
A _______ spans a geographic area like a city,is larger than a LAN and smaller than WAN

Answers

Answer:

metropolitan area network (MAN)

Explanation:

A local area network (LAN) refers to a group of personal computers (PCs) or terminals that are located within the same general area and connected by a common network cable (communication circuit), so that they can exchange information from one node of the network to another. A local area network (LAN) is typically used in small or limited areas such as a set of rooms, a single building, school, hospital, or a set of well-connected buildings.

On the other hand, a metropolitan area network (MAN) spans a geographic area like a city, is larger than a local area network (LAN) and smaller than wide area network (WAN).

Basically, a metropolitan area network (MAN) is formed by an aggregation of multiple local area network (LAN) that are interconnected using backbone provided by an internet service provider (ISP). A metropolitan area network (MAN) spans for about 5 kilometers to 50 kilometers in size.

What is market information?

please answer in your own words since my teacher will probably notice if I plagerize

Answers

Answer:

Market information is is the understanding of the trends going on in a market such as demographic popular product age interests things like that

Explanation:

17.35 ma of current is flowing though a brown-red-brown resistor,what is v

Answers

Answer:

2.1V

Explanation:

brown-red-brown = 120Ω

V = I·R = 17.35 · 120 = 2.082V

However, the tolerance of the resistor is at least 10%, so you can't express the voltage that accurate.

Write a structured algorithm that prompts the
user to input two numbers. The algorithm should
multiply both numbers and then prompt the
user to enter the answer. The algorithm should
compare the answer entered with that calculated
and output "correct answer" or "incorrect answer"
accordingly. At the start, input how many sums
will be done.

Answers

Answer:

Step 1 : Start

Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

Explanation:

Algorithm is a sequence of instructions a computer is expected to follow to solve a particular problem.

Required :

Two inputs ; num1 and num2

Expected output

Algorithm :

Step 1 : Start

Step2 : Input first number, num1

Step3 : Input second number, num2

Step4 : product - - > num1 * num2 (product of num1 and num2)

Step5 : Input product, myanswer

Step6 : comparison - - - > correct or incorrect based on myanswer and product

Step6: print(comparison)

Step7: End

The two numbers to multiply are entered ; the product is calculated by the program ; the the user inputs his or her own expecteted product ;

Both are compared and the output of the comparison is displayed (either correct oe incorrect)

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Answers

A. True
B. False
C. True

If you see rough patches, loose,gravel,or potholes on the road you should

Answers

Answer:

move out of the way

Explanation:

Drive around them in the safest way as possible. if that is not an option then turn around in a nearby parking lot of some sort and take another road to your destination

How do you reset a g.mail password?

Answers

Answer:

put: forgot password to reset it

Answer:

Change your pass word

Open your Go ogle Account. You might need to sign in.

Under "Security," select Signing in to G oo gle.

Choose Password. You might need to sign in again.

Enter your new password, then select Change Password.

The cultivation in mountain areas, with their scattered plots of usable land at various altitudes with different climates, landscapes and little margin for mechanization, are managed by family farms in the most efficient and effective way.

Answers

Answer:

Mountain farming

Explanation:

Mountain farming is done in hilly areas of the mountains. It is mainly family farming. The mountain farming is mainly done in the mountains where the paddy fields are scattered and the limited use of the usable lands are available.

It is cultivated in different types of climatic conditions or landscapes with limited use of mechanization or machines. The mountain farming is maintained by the family farms in an effective way.

who invented the system of logarithm in 1614 AD​

Answers

Answer:

JOHN NAPIER

Explanation:

The method of logarithms was publicly propounded by John Napier in 1614, in a book entitled Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Rule of Logarithms). The book contained fifty-seven pages of explanatory matter and ninety pages of tables related to natural logarithms.

Answer:

Joost Bürgi

Explanation:

He invented it but John Napier worked on it earlier than Bürgi.

what are the advantages of saving files in a cloud?
Please help!! ​

Answers

When using cloud storage, one of its main advantages is the accessibility and its ability to not get deleted as easily. Once a file is uploaded to the cloud, you can access it from almost any device as long as you have connection. And it’s not as easy from something to get accidentally deleted, as there is a backup.

What are the uses of DVD Ram​

Answers

Answer:

Like ordinary random access memory (RAM), it can be repeatedly read, written to, and erased. Intended mostly for removable computer storage, DVD-RAM provides the capabilities of Rewriteable CD (CD-RW) - users can run programs from the discs, copy files to them and rewrite or delete them.

DVD Ram Like ordinary random access memory (RAM), it can be repeatedly read, written to, and erased. Intended mostly for removable computer storage, DVD-RAM provides the capabilities of Rewriteable CD (CD-RW) - users can run programs from the discs, copy files to them and rewrite or delete them.

it is used to hold screws, jumpers, fasteners, and other small parts and prevent them from getting mixed together​

Answers

Answer:

Cable ties

Explanation:

Used to bundle cables neatly inside and outside of a computer. It is used to hold screws, jumpers, fasteners, and other small parts and prevent them from getting mixed together.

>3

[tex]\boxed{Parts\: organizer}[/tex] is used to hold screws, jumpers, fasteners, and other small parts and prevent them from getting mixed together.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Which scenario would most benefit from a self-join query?
a. a query connecting customers and products
b. a query connecting supervisors and customers
c. a query connecting employees and their orders
d. a query connecting employees and their supervisors

Answers

Answer:

answer is D

Explanation:

Just did it on edge

what do you mean by professional education? explain with examples.​

Answers

Answer:

prfesssional education is any programs that improve the knowledge,skills and attitudes.

Example include; educational course and training to become a teacher,nursing course,aeronautics engineering,etc.

I copied my friend's homework... give me some excuses to get out of it!! ​

Answers

Answer:

Tell the teacher that you will pee in her coffee cup if they don't forget about what you did

Explanation:

Answer:

Explanation:

Depends on the homework, but

"We worked together on it and came to similar conclusions."

"We checked answers with each other when we finished to make sure we got the problems correct and did the problems correctly."

sign that your desktop may need cleaning​

Answers

Answer:

My desktop may need be cleaning but for real!!

how is a trade off best described ?

dilema
compromise
demand
complication

Answers

I think the answer is compromise <3

Which is an example of a table style option?

O banded columns

O shading

O borders

O pen color

PLEASE HELP ASAP

Answers

Which is an example of a table style option?

O banded columns

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

how to prevent water pollution​

Answers

Answer:

Here is your answer

Explanation:

1. pick up litter and throw it away in a garbage can.

2. use environmentally household products such as washing powder, household cleaning agents

3. wash your car or outdoor equipment where it can flow to a gravel or grassed area instead of a street.

4. don't throw waste at ocean it will harm the animals and create tocsin.

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