Given that 7 cos 2 + 24 sin 2 R cos (2 ), where R > 0 and 0 < <

Given that 7 cos 2θ + 24 sin 2θ ≡ R cos (2θ − α), where R > 0 and 0 < α < π < 2 , find:

a. The value of R and the value of α, to 2 decimal places.

b. The maximum value of 14 cos2 θ + 48 sin θ cos θ.

c. Solve the equation 7 cos 2θ + 24 sin 2θ = 12.5, for 0 ≤ θ ≤ 180°, giving your answers to 1 decimal place.