Express '6cos(2x) +sin(x)' in terms of sin(x).

6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin^2(x)) + sin(x). Now use the trigonometric identity 1 = cos^2(x) + sin^2(x).6(cos^2(x) - sin^2(x)) + sin(x) = 6((1-sin^2(x)) - sin^2(x)) + sin(x) .6((1-sin^2(x)) - sin^2(x)) + sin(x) = 6 (1 - 2sin^2(x)) +sin(x) .Therefore, 6cos(2x) +sin(x) = 6 + sin(x) -12sin^2(x).6cos(2x) +sin(x) = (4sin(x) − 3)*(3sin(x) + 2)