Precalculus (6th Edition) Blitzer

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

Chapter 5 - Mid-Chapter Check Point - Page 683: 7


See the explanation below.

Work Step by Step

The left side of the expression $\frac{\sin x}{\tan x}+\frac{\cos x}{\cot x}$ can be further simplified by using the quotient identities $\tan x=\frac{\sin x}{\cos x}$ and $\cot x=\frac{\cos x}{\sin x}$. $\begin{align} & \frac{\sin x}{\tan x}+\frac{\cos x}{\cot x}=\frac{\sin x}{\frac{\sin x}{\cos x}}+\frac{\cos x}{\frac{\cos x}{\sin x}} \\ & =\sin x.\frac{\cos x}{\sin x}+\cos x.\frac{\sin x}{\cos x} \\ & =\cos x+\sin x \end{align}$ Hence, the left side is equal to the right side $\frac{\sin x}{\tan x}+\frac{\cos x}{\cot x}=\sin x+\cos x$.
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