Question

How do you verify `(1-cos^2a)(1+cos^2a)=2sin^2a-sin^4a`?

Answer 1

Prove trig identity

Explanation:

Use the trig identity: sin^2 a + cos^2 a = 1
Left side of the equation:
`LS = (1 - cos^2 a)(1 + cos^2 a) = sin^2 a(1 + cos^2 a) =`
`= sin^2 a + sin^2 a.cos^2 a = sin^2 a + sin^2a(1 - sin^2 a) =`
`= 2sin^2 a - sin^4 a`