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: 44



Work Step by Step

$$A=\cos(90^\circ-\theta)$$ Apply the cosine difference identity, which states $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ we have $$A=\cos90^\circ\cos\theta+\sin90^\theta\sin\theta$$ $$A=0\times\cos\theta+1\times\sin\theta$$ $$A=\sin\theta$$ which is actually the proof of cofunction identity for $\sin\theta$: $$\sin\theta=\cos(90^\circ-\theta)$$
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