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Chapter 7: Q. 41 (page 504)

Establish each identity
1-8sin2胃cos2胃=cos4胃

Short Answer

Expert verified

The derivation of the equation1-8sin2胃cos2胃=cos4胃is

1-8sin2胃cos2胃=1-2(2sin胃cos胃)2=1-2sin2(2胃)=cos(4胃)

Step by step solution

01

Step 1. Given data

The given equation for derivation is

1-8sin2胃cos2胃=cos4胃

02

Step 2. Proof

Take left-hand side expression and use double angle formula for the sine function

1-8sin2胃cos2胃=1-2(2sin胃cos胃)2=1-2sin2(2胃)

Use double angle formula for the cosine function

1-8sin2胃cos2胃=1-2sin2(2胃)=cos(4胃)

The left-hand side expression is equal to the right-hand side expression

So identity is stabilised

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