Question

How do you verify `sin^2 theta cos ^2 theta = 1/8 [1-cos(4 theta)]`?

Answer 1

Use trig identities: `2sin a.cos a = sin 2a`
and `2sin^2 a = 1 - cos 2a`

`sin^2 a.cos^2 a` = `(1/4)(sin^2 2a)` = `(1/8)(2sin^2 2a)` =

`= (1/8)(1 - cos 4a)`