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: 21

Answer

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

Work Step by Step

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