Question

Simplify `sin^4x-cos^4x+cos^2x`?

Answer 1

The answer is `=sin^2x`

Explanation:

We need

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

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

`a^4-b^4=(a^2+b^2)(a^2-b^2)`

The expression is

`sin^4x-cos^4x+cos^2x`

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

`=(sin^2x-cancelcos^2x)+cancelcos^2x`

`=sin^2x`

Answer 2

`sin^4x-cos^4x+cos^2x=sin^2x`

Explanation:

`sin^4x-cos^4x+cos^2x`

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

= `sin^2x-cos^2x+cos^2x`

= `sin^2x`