Question

Sin^2(x)-cos^2(x)= sin^2(x)+cos^2(x) Find exact solutions between 0 and 2π How should I solve this?

Answer 1

`pi/2 ; (3pi)/2`

Explanation:

`sin^2 x - cos^2 x = sin^2 x +cos^2 x = 1`
Replace `cos^2 x` by `(1 - sin^2 x)`:
`sin^2 x - 1 + sin^2 x = 1`
`2sin^2 x =2` --> `sin^2 x = 1` -->
`sin x = +- 1`
Unit circle gives -->
`x = pi/2 and x = (3pi)/2`