Rewrite the expression so that it involves the sum or difference of only constants and sines and cosine to the 1st power

Question

(sinx)^4

Answer 1

sin^4
(1-cos^2)^2
(1-cos)^2(1+cos)^2
(1-cos)(1-cos)(1+cos)(1+cos)

sin^2(x) = (1-cos(2x))/2
so,
sin^4(x) = (1 - cos(2x))^2/4
= (1 - 2cos(2x) + cos^2(2x))/4
= (1 - 2cos(2x) + (1 - cos(4x))/2)/4
= (1 - 2cos(2x) + 1/2 - cos(4x)/2)/4
= (2 - 4cos(2x) + 1 - cos(4x))/8
= (3 - 4cos(2x) - cos(4x))/8

don't know which way you wanted to go there.