Question

Prove that cos 8theta minus sin 8 theta equal to cos squared theta minus sin squared theta x 1 - 2 sin square theta cos square theta

Answer 1

$\sin( \alpha ) {}^{2} + \cos( \alpha ) {}^{2} = 1$
$(x + y)(x - y) = x { }^{2} - y {}^{2}$
(cos4-sin4)(cos4+sin4)
(cos²-sin²)(sin²+cos ²)(cos²+sin²)²-2sin²cos²)
(cos²-sin²)((cos²+sin²)²-2sin²cos²)
(cos²-sin²)(1²-2sin²cos²)