Given that p(x) = R cos (2 + ), where R > 0 and 0 < < 90, p(x) = 12 cos 2

Given that p(x) = R cos (2θ + α), where R > 0 and 0 < α < 90°, p(x) = 12 cos 2θ − 5 sin 2θ.

a. Find the value of R and the value of α.

b. Hence solve the equation 12 cos² θ − 5 sin 2θ = −6.5 for 0 ≤ α < 180°. 

c. Express 24 cos² θ − 10 sin θ cos θ in the form a cos² θ + b sin 2θ + c, where a, b and c are constants to be found.

d. Hence, or otherwise, find the minimum value of 24 cos² θ − 10 sin θ cos θ.