1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mrac [35]
2 years ago
9

Proving trigonometric identities 2(cosx sinx-sinx cos2x)/sin2x =secx

Mathematics
1 answer:
eduard2 years ago
3 0

This is not an identity.

\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)

Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.

Keeping the left side unchanged, the correct identity would be

\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)

To show this, recall

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = cos²(x) - sin²(x)

• cos²(x) + sin²(x) = 1

Then we have

\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)

You might be interested in
52 lbs is equal to how many kg
Butoxors [25]
1 lb  = 0.45 kg
52 lb= 0.45 * 52
52 lb= 23.4 kg



4 0
3 years ago
Read 2 more answers
Identify each expression as linear or nonlinear.<br><br> 8xy. Please answer
-BARSIC- [3]

Answer:

I want to help but I don't understand the question. Can you plz send a picture of the question

8 0
3 years ago
Please help me fast.
dlinn [17]
It is c have a nice rest of your day.
5 0
3 years ago
Read 2 more answers
Help plz (please don’t answer saying A or B. That answer makes 0 sense...stop) thx
Anuta_ua [19.1K]
Hey there! :D

Think of it this way. The question is saying that the text messages are all equally the same value, or expense. If you were to divide 16 by $3.20, you would find that each text was the same amount to send. That the input (the number of text messages) is directly related in the same pattern to the output (the cost of the text messages). 

A. What is the constant of proportionality in this proportional relationship? 

A constant of proportionality is what makes x directly relate in proportion to y.  We are trying to find the variable that makes y= (?)x

16y= 3.20x

Divide both sides by 16. 

y=0.20x or y=0.2x 

The constant is the value that goes with the variable. .20 is the constant. '

B. Write an equation to represent this proportional relationship. Make sure to define the variables you use. 

We already know that 0.20 is the constant number. In other words, every text message cost $.20. 

Text messages= T cost= C

C= T(0.20) 

For every text message (T), it is multiplied by 0.20, to make the accurate cost (C). 

I hope this helps!
~kaikers

8 0
3 years ago
Read 2 more answers
What is the 18th term for the following sequence?<br><br> -3, 1, 5, 9, 13,
pochemuha

Answer: The Answer is 72

Step-by-step explanation:

It is quite easy if you think about it.

first you must find the rule and the pattern.

Once you find that just multiply 18 by how much of a difference there is.

The difference is 4. You must add 4.

3 0
3 years ago
Other questions:
  • What is the minimum cuts<br> needed to cut a circle into 8<br> equal parts?
    7·2 answers
  • A survey found that 12 out of every 15 people in the united States prefer eating at a restaurant over cooking at home. if 400 pe
    11·2 answers
  • I need help please ASAP im gonna fail if i dont get right will give 51 points
    13·1 answer
  • The perimeter of Dawna's new flat screen television is 70 inches. The ratio of its length to width is 4:3. Write and solve an al
    12·2 answers
  • ASAP What is the slope of the line y= 3?
    5·2 answers
  • CAN SOMEONE PLZ HELPP
    6·1 answer
  • Graph this line using the slope and intercept <br> -1/9x-8
    15·1 answer
  • PLS HELP!! IM BEGGING OF YOU! SELECTING BRAINLIEST!!
    15·1 answer
  • What does 58x9234=????
    5·1 answer
  • Learning Task 3: Read and interpret the graph. Answer the questions that follow on your pape School Books English Math 20 80 60
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!