Question

cos (4theta)= cos^4 - 6sin^2cos^2 + sin^4

Answer 1

cos(4x) = cos(2x+2x)
             = cos²(2x)-sin²(2x)
             = [cos(x+x)]²-[sin(x+x)]²
             = [cos²x-sin²x]²-4sin²(x)cos²(x)
             = cos⁴(x)-cos²(x)sin²(x)-cos²(x)sin²(x)+sin⁴(x)-4sin²(x)cos²(x)
             = cos⁴(x)-6sin²(x)cos²(x)+sin⁴(x)