Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 67


$$\cos(\frac{\pi}{2}+x)=-\sin x$$ The formula is verified to be an identity.

Work Step by Step

$$\cos(\frac{\pi}{2}+x)=-\sin x$$ According to the identity of cosine of a sum, we can analyze the left side as follows: $$\cos(\frac{\pi}{2}+x)$$ $$=\cos\frac{\pi}{2}\cos x-\sin\frac{\pi}{2}\sin x$$ $$=0\times\cos x-1\times\sin x$$ $$=-\sin x$$ Which means the left side is equal with the right side. So the formula is verified to be an identity.
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