Question

Simplify (1 − cos x)(1 + cos x). (2 points)

Answer 1

`sin^2x`

Explanation:

Given expression,

`(1 - cos x)(1 + cos x)`

By using
`a^2-b^2=(a+b)(a-b)`

`(1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x`

`\because sin^2x+cos^2x=1`

`\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x`

Since, further simplification is not possible,

Hence, the simplified form of the given expression is
`sin^2x`

Answer 2

sin²x

Explanation:

we have

(1 − cos x)(1 + cos x)=1-cos²x

Remember that

sin²x+cos²x=1 ------> i-cos²x=sin²x

therefore

(1 − cos x)(1 + cos x)=sin²x