Use the power reducing formulas to rewrite tanx cosx in term

Use the power reducing formulas to rewrite tan\'x cos\'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. O tan x cos x tanx cos\'xcos

Solution

tan²x cos⁴x

(sin²x/cos²x)cos⁴x

sin²xcos²x

(1-cos²x)cos²x

cos²x -cos⁴x

(cos(2x)+1)/2 -((cos(2x)+1)/2)²

(cos(2x)+1)/2-(cos²2x +1+2cos 2x)/4

1/4 - cos²2x/4 =1/4 -1/4(2 cos 4x +1)/2= 1/8- cos(4x)/8