Cos2x + sin^2(x) = 1/2 help solve for the idntity

Question

Help please

Answer 1

Cos2x + sin^2(x) = 1/2

If the first trig function has argument 2x but the second trig function is the square of (sin x), then this is NOT AN IDENTITY; it's a conditional equation that is only true for certain values.  To find them,

replace cos 2x by  1 - sin²x.

 

Now you have a quadratic equation (in sin x) and that can be solved, probably by factoring.  (It might help you to let u = sin x for the quadratic solving step.)