Write an equivalent expression for 6 sin^4 𝑥 that does not contain powers of trigonometric functions greater than 1

Question

the x is not raised to the power of 6

Answer 1

sin^4(x) = sinx(sinx)(sinx)(sinx) which has no exponent greater than 1

or

cos2x =1-2sin^2(x)

2sin^2(x) = cos2x-1

sin^2(x) =(cos2x-1)/2

sin^4(x) = (sin^2(x))(sin^2(x)) = (1/4)(cos2x-1)^2 =(1/4)(cos^2(2x)-2cos2x+1)

= (1/4)((cos4x+1)(1/2) -2cos2x +1)=(cos4x)/8 + 1/8 -(cos2x)/2 + 1/4

= cos(4x)/8 -(cos2x)/2 +3/8

6sin^4(x) = (3/4)cos4x -3cos2x + 9/4