# if cos(angle)=-sin (angle) then what is sin^2(angle) ?

### 2 Answers | Add Yours

`cos(angle) = -sin(angle)` when `angle = (3pi)/4` and `(7pi)/4`

`sin(angle) = +-1/2`

so `sin^2(angle) = 1/4`

let angle be A

now cosA=-sin A

squaring both sides,

cos^2A=sin^2A

or, 1-sin^2A=sin^2A

or, 1=2sin^2A

or 1/2=sin^2A

Therefore, in the given condition, sin ^2 (angle) =1/2