Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.1 - Proving Identities - 5.1 Problem Set - Page 279: 20

Answer

As left side transforms into right side, hence given identity- $\sin x (\sec x + \csc x)$ = $\tan x + 1$ is true.

Work Step by Step

Given identity is- $\sin x (\sec x + \csc x)$ = $\tan x + 1$ Taking L.S. $\sin x (\sec x + \csc x)$ = $\sin x (\frac{1}{\cos x} + \frac{1}{\sin x})$ ( Using reciprocal identities) = $\frac{\sin x}{\cos x} + \frac{\sin x}{\sin x}$ = $\tan x + 1$ = R.S. As left side transforms into right side, hence given identity- $\sin x (\sec x + \csc x)$ = $\tan x + 1$ is true.
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