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Chapter 5: Q 6. (page 495)

Use Pythagorean identities to rewrite each of the following trigonometric expressions.

csc8x=____

Short Answer

Expert verified

The obtained result is 11-cos2x4.

Step by step solution

01

Step 1. Given information.

Consider the given expression.

csc8x

02

Step 2. Apply the Pythagorean identities to rewrite the expression.`

The Pythagorean identity is defined as,

sin2x+cos2x=1

Use the identity to write the given expression.

sin2x=1-cos2xsin2x4=1-cos2x4sin8x=1-cos2x41sin8x=11-cos2x4csc8x=11-cos2x4

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