Question

sin^2x=cosx

Answer 1

Do you know the double angle identity relating sin^2x and cos squared?

Answer 2

sin^2x=cosx we know that sin^2x = 1-cos^2x.

So, lets substitute,

sin^2x=cosx
1-cos^2x=cosx subtract cos(x) from both sides
1-cos^2x-cos(x)=0 now, re-write from biggest to smallest power.
-cos^2x-cos(x)+1=0 multiply everything times -1.
cos^2x+cos(x)-1=0

let cos(x)=a, So...

a^2+a-1=0

can you take it from here ?