Use the power reducing formulas to rewrite sin4 x in terms o

Use the power reducing formulas to rewrite sin^4 x in terms of the first power of cosine. Simplify your answer as much as possible. To indicate your answer, first choose one of the four forms below. Then fill in the blanks with the appropriate numbers.

Solution

sin^4x = sin^2x*sin^2x

now we know that sin^2x = 1-cos^2x

sin^4x = sin^2x*sin^2x = ( 1-cos^2x)( 1-cos^2x)

= 1 - cos^2x -cos^2x +cos^4x

= 1 -2cos^2x +cos^4x