Question

Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1: 10sin^4x

Answer 1

10 sin^4x

we know

sin²x = (1-cos(2x))/2

10((1-cos(2x))/2)²

10/4*(1-cos(2x))²

5/2*(1+cos²2x-2cos(2x))

we know

cos²x = (1+cos(2x))/2

5/2*(1+(1+cos4x)/2-2cos(2x))

5/2*(3/2+cos(4x)/2-2cos(2x))

15/4+5/4cos(4x)-5cos(2x)