Question

Prove that `cot^2x-cos^2x=cot^2xcos^2x`?

Answer 1

Please see below.

Explanation:

`cot^2x-cos^2x`

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

= `(cos^2x-cos^2xsin^2x)/sin^2x`

= `(cos^2x(1-sin^2x))/sin^2x`

= `(cos^2x xxcos^2x)/sin^2x`

= `(cos^2x/sin^2x xxcos^2x)`

= `cot^2xcos^2x`

Answer 2

Develop the left side:
`LS = (cos^2 x)/(sin^2 x) - cos ^2 x = ((cos^2 x)(1 - sin^2 x))/(sin^2 x) =`
`= (cos^2 x.cos^2 x)/(sin^2 x) = cot^2 x.cos^2 x` Proved.