Question

cos^6theta + sin^6theta = 1 - 3cos^2 theta sin^2theta

Answer 1

HELLO THERE!

If your question is to prove the above identity, here is your answer:

LHS:

$cos^{6}\theta + sin^{6}\theta \\\\ = (cos^{2}\theta)^{3} + (sin^{2}\theta)^{3} \\\\= (cos^{2}\theta+sin^{2}\theta)^{3} - 3.cos^{2}\theta.sin^{2}\theta(cos^{2}\theta + sin^{2}\theta) \\\\= 1 - 3cos^{2}\theta sin^{2}\theta$

Formulas used:

a³ + b³ = (a + b)³ - 3ab (a + b)

sin²θ + cos²θ = 1

Thanks!