Question

Prove that
cos^4∆ - sin^4∆ = 2cos^2∆ - 1

Answer 1

`\cos^(4) x-\sin^(4) x\\\\=(\cos^(2) x+\sin^(2) x)(\cos^(2) x-\sin^(2) x)\\\\=\cos^(2) x-\sin^(2) x\\\\=\cos^(2) x-(1-\cos^(2) x)\\\\=2\cos^(2) x-1`