Question

Simplify the expression by using a double-angle formula or a half-angle formula.

7cos^2(theta/9)-7sin^2(theta/9)
sin(theta/6)cos(theta/6)

Answer 1

Double-angle formulas:
2sinФcosФ=sin(2Ф) /:2
sinФcosФ=1/2*sin(2Ф)

sin(Ф/6)cos(Ф/6)=1/2*sin(2*Ф/6)=1/2*sin(Ф/3)

cos²Ф-sin²Ф=cos(2Ф)/*7
7cos²Ф-7sin²Ф=7cos(2Ф)

7cos²(Ф/9)-7sin²(Ф/9)=7cos(2*Ф/9)=7cos(2Ф/9)