Show that $\sin^2 2x + 4\cos^2 x \cos 2x = 4\cos^4 x$.
(b)[2]
Determine the set of values of the constant $k$ for which the equation $\sin^2 2x + 4\cos^2 x \cos 2x + 5 = k$ has no real solutions.
(c)[4]
Find the exact value of $\int_{-\frac{\pi}{3}}^{\frac{\pi}{3}} \sqrt{\sin^2 t + 4\cos^2\left(\frac{t}{2}\right)\cos t}\,dt$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply suitable identities to rewrite the expression in terms of $\sin x$ and $\cos x$” …