   Chapter 1.5, Problem 69E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Prove that cos ( sin − 1 x ) = 1 − x 2 .

To determine

To prove: The equality of cos(sin1x)=1x2 .

Explanation

Given:

The equation is cos(sin1x)=1x2 .

Proof:

Squaring on both sides yields, cos2(sin1x)=1x2

Express the cosine function in terms of sine function such as cos2x=1sin2x .

Thus, 1sin2(sin1x)=1x2 .

Simplify the above equation as follows.

1(sin(sin1x))2=1

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