Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.4 - Mathematical Induction - Exercise Set - Page 1086: 49


See the full explanation below.

Work Step by Step

By solving the left side of the identity, we get: $\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$: $\begin{align} & \cot x+\tan x=\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x} \\ & =\frac{{{\cos }^{2}}x+{{\sin }^{2}}x}{\sin x\cos x} \\ & =\frac{1}{\sin x\cos x} \\ & =\frac{1}{\sin x}\times \frac{1}{\cos x} \end{align}$ Therefore, $\cot x+\tan x=\left( \csc x \right)\left( \sec x \right)$ Thus, the solution is that the identity is correct.
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