Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5: 37

Answer

The statement is true.

Work Step by Step

If we divide both sides of equality $f(x)\cos x=\sin x$ with $\cos(x)$ we get that $f(x)=\frac{\sin x}{\cos x}=\tan x$. Now it is easy to see that $$f'(x)=(\tan x)'=\sec^2x$$ So, the statement is true.
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