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)

Double-angle formulas:

2sinФcosФ=sin (2 Ф) / : 2

sinФcosФ=1/2*sin (2 Ф)

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

cos²Ф-sin²Ф=cos (2 Ф) / * 7

7cos²Ф-7sin²Ф=7cos (2 Ф)

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