Question

How do you prove `8sin^2thetacos^2theta = 1-cos^4theta`?

Answer 1

The given identity is false.

Explanation:

Let `theta = pi/2`

Then `8sin^2(pi/2)cos^2(pi/2) = 8(1)^2(0)^2 = 8(1)(0)=0`

But `1-cos^4(pi/2) = 1-0^4 = 1-0 = 1`