`2 sin^2x -1 = sin^2 x- cos^2 x`
Let us start with the left hand side of the equation.
Using the identity, `sin^2 x + cos^2 x = 1 `
we get: `2sin^2 x - 1 = 2sin^2x - (sin^2x + cos^2x) = 2sin^2 x - sin^2 x - cos^2x`
`= sin^2 x - cos^2 x`
which is the right hand side of the given question. Hence proved.