Question

Hi, how do i prove Sin^2x/1+cosx=1-cosx? Any help is amazing! Thank you

Answer 1

See below

Explanation:

`sin^2x/(1+cosx)=1-cosx`

Transpose the expresion `1+cosx` to the right side

`sin^2x=(1-cosx)(1+cosx)`

Remember the notable expresion `(a+b)(a-b)=a^2-b^2`

Apply this to the right term

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

But we know that `sin^2x+cos^2x=1` then `1-cos^2x=sin^2x`

And finally we prove the identity proposed