Prove the following identity: cos4x - sin4xcot2x = -1

We have to prove that cos 4x - sin 4x * cot 2x =
-1

cos 4x - sin 4x * cot 2x =
-1

use cos 2x = (cos x)^2 - (sin x)^2 and sin 2x = 2 sin x
cos x and cot x = (cos x)/(sin x)

=> (cos 2x)^2 -
(sin x)^2 - 2*(sin 2x)*(cos 2x)*(cos 2x)/(sin
2x)

=>(cos 2x)^2 - (sin x)^2 - 2*(cos 2x)*(cos
2x)

=> ( cos 2x)^2 - 2 ( cos 2x)^2 - ( sin
2x)^2

=> - (cos 2x)^2 - (sin
2x)^2

=> -1*[(cos 2x)^2 + (sin
2x)^2]

As (cos x)^2 + (sin x)^2 =
1

=> -1

Therefore we
proved that

cos 4x - sin 4x *
cot 2x = -1