a) Prove the identity: (cos θ)/(1 - sin θ) - (cos θ)/(1 + sin θ) = 2 tan θ. b) i) Express 3 sin x + 4 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the values of R and α correct to 2 decimal places where necessary. ii) Hence find the maximum value of the expression 1/(7 + 3 sin x + 4 cos x) and state the value of x in the range 0° ≤ x ≤ 360° at which it occurs. c) Solve the equation 2 cos² θ - sin θ - 1 = 0 for 0° ≤ θ ≤ 360°.