Question

How do you prove `Sin^2-cos^2=2sin^2-1` ?

Answer 1

Replace in the equation `cos^2 x` by `(1 - sin^2 x)`

We know this is true through manipulation of the Pythagorean identity:

`sin^2x+cos^2x=1" "=>" "cos^2x=1-sin^2x`

`sin^2 x - (1 - sin^2 x) = 2sin^2 x - 1.`