Use the powerreducing formulas to rewrite the expression as

Use the power-reducing formulas to re-write the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

7 sin^4 x=

(simplify your answer. Use integers or fractions for any numbers in the expression.)

Solution

7sin^4x

use the double angle indentity : 2sin^2x = 1- cos2x

So, 7 (sin^2x)^2

= 7(1 -cos2x)^2/4

= (7/4)(1 +cos^2(2x) -2cos2x )

= 7/4 + 7cos^2(2x)/4 - 7cos2x/2

= 7/4 + (7/4)(1+cos4x)/2 - (7/2)cos2x

= 7/4 + (7/8) + (7/8)cos4x - (7/2)cos2x

= 21/8 + (7/8)cos4x - (7/2)cos2x