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 5.1 Fundamental Identities - 5.1 Exercises - Page 201: 39


$$-\tan x\cos x=\sin(-x)$$ $\text{C}$ is the answer.

Work Step by Step

$$A=-\tan x\cos x$$ A Quotient Identity related to $\tan x$ states that $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ That means we can rewrite $A$ as follows: $$A=-\frac{\sin x}{\cos x}\cos x$$ $$A=-\sin x$$ Also, from Negative-Angle Identities, we know $$\sin(-\theta)=-\sin\theta$$ Therefore, $$A=\sin(-x)$$ $\text{C}$ is the answer.
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