Question

Prove the identity
sin ^2cos^2= 1/8(1-cos 4x)

Answer 1

i think ur problem is incomplete.

Answer 2

why?

Answer 3

the original was : rewrite sin ^2cos^2 using the power reducing formulas and 1/8(1-cos 4x) was the answer in the book; i dont know how to get there.

Answer 4

sin^2cos^2 has no variable x and the answer includes x? how come?

Answer 5

sin^2xcos^2x sorry

Answer 6

okay....
cos 2x = cos^2 x - sin^2 x
cos 2(2x) = cos^2 (2x) - sin^2 (2x)
cos 4x = cos^2 (2x) - sin^2 (2x) eqn 1

sin^2 2x + cos^2 2x = 1
cos^2 2x = 1 - sin^2 2x eeqn 2

substitute eqn 2 to eqn 1:
cos 4x = (1 - sin^2 2x) - sin^2 (2x)
cos 4x = 1 - 2sin^2 2x
2sin^2 2x = 1 - cos 4x
sin^2 2x = (1 - cos 4x)/2 eqn 3

sin 2x = 2sin x cos x
sin x cos x = (sin 2x)/2
sin^2 x cos ^2 x = (sin^2 2x)/4 eqn 4

subst eqn 3 to eqn 4
sin^2 x cos ^2 x = ((1 - cos 4x)/2)/4
sin^2 x cos ^2 x = ((1 - cos 4x)/8 proven!

Answer 7

Thanks!