1+cos 2x 11. = cot x sin 2x HINT: If the first cosine double angle formula you try doesn't work, try another.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Help me prove the identity please
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**Trigonometric Identities and Equations**

**Problem 11:** 

\[ \frac{1 + \cos 2x}{\sin 2x} = \cot x \]

**HINT:** If the first cosine double angle formula you try doesn't work, try another.

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**Explanation:** 

In this problem, you are required to verify the trigonometric identity given. The hint suggests that there may be multiple identities for the cosine double angle, so you should be prepared to try different forms if your initial approach doesn't simplify the expression as expected.

Remember the double angle identities for cosine:

1. \(\cos 2x = \cos^2 x - \sin^2 x\)
2. \(\cos 2x = 2\cos^2 x - 1\)
3. \(\cos 2x = 1 - 2\sin^2 x\)

Also recall the identity for \(\sin 2x\):

\[ \sin 2x = 2\sin x \cos x \]

By using these identities appropriately, you can simplify the given expression to verify that it equals \(\cot x\).

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Transcribed Image Text:--- **Trigonometric Identities and Equations** **Problem 11:** \[ \frac{1 + \cos 2x}{\sin 2x} = \cot x \] **HINT:** If the first cosine double angle formula you try doesn't work, try another. --- **Explanation:** In this problem, you are required to verify the trigonometric identity given. The hint suggests that there may be multiple identities for the cosine double angle, so you should be prepared to try different forms if your initial approach doesn't simplify the expression as expected. Remember the double angle identities for cosine: 1. \(\cos 2x = \cos^2 x - \sin^2 x\) 2. \(\cos 2x = 2\cos^2 x - 1\) 3. \(\cos 2x = 1 - 2\sin^2 x\) Also recall the identity for \(\sin 2x\): \[ \sin 2x = 2\sin x \cos x \] By using these identities appropriately, you can simplify the given expression to verify that it equals \(\cot x\). ---
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