1) Use double-angle identities to write the following expression, using trigonometric functions of x instead of 4x.

Question

cos 4x

2) Use half-angle identities to write the following expression, using trigonometric functions of x instead of x/4.

sin x/4

Answer 1

cos4x = 2cos^2(2x)-1
= 2(2cos^2(x)-1)^2 - 1
just expand that

sin(x/4) = sqrt((1-cos(x/2))/2)
= sqrt((1-sqrt((1-cos(x))/2)/2