Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 212: 3

Answer

For an identity to be made, 3 should be matched with E.

Work Step by Step

According to the given identity, we have that $$\cos(x-y)=\cos x\cos y+\sin x\sin y$$ Now apply to the case in third expression: $$\cos(\frac{\pi}{2}-x)=\cos(\frac{\pi}{2})\cos x+\sin(\frac{\pi}{2})\sin x$$ $$=0\times\cos x+1\times\sin x$$ $$=\sin x$$ Now we match with the expressions in II. We find that the third expression in I matches the expression E in II. Therefore, we would match 3 with E to have an identity.
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