Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x 1+cos x 土, 2 b. cos - 1-cos x c. sin =±, 2
Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x 1+cos x 土, 2 b. cos - 1-cos x c. sin =±, 2
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°.
Related questions
Question
![Derive/Prove:
\[
\sin 2x = 2 \sin x \cos x
\]
- Useful Formula:
\[
\cos 2x = \cos^2 x - \sin^2 x
\]
a.
\[
= 2 \cos^2 x - 1
\]
\[
= 1 - 2 \sin^2 x
\]
b.
\[
\cos \frac{x}{2} = \pm \sqrt{\frac{1 + \cos x}{2}}
\]
c.
\[
\sin \frac{x}{2} = \pm \sqrt{\frac{1 - \cos x}{2}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b727f25-8808-4b74-9fb9-f2e74344edb6%2F4753a05b-340b-4e9b-b5cc-8ace075ee69b%2Fj6lpo5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Derive/Prove:
\[
\sin 2x = 2 \sin x \cos x
\]
- Useful Formula:
\[
\cos 2x = \cos^2 x - \sin^2 x
\]
a.
\[
= 2 \cos^2 x - 1
\]
\[
= 1 - 2 \sin^2 x
\]
b.
\[
\cos \frac{x}{2} = \pm \sqrt{\frac{1 + \cos x}{2}}
\]
c.
\[
\sin \frac{x}{2} = \pm \sqrt{\frac{1 - \cos x}{2}}
\]
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