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Chapter 5: Q 2. (page 495)

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

cos4x=_____

Short Answer

Expert verified

The obtained result is1+sin4x-2sin2x.

Step by step solution

01

Step 1. Given information.

Consider the given expression.

cos4x

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.

localid="1651821571277" role="math" sin2x+cos2x=1cos2x=1-sin2xcos2x2=1-sin2x2cos4x=1+sin4x-2sin2x

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