Express $3\\cos x + 2\\cos(x - 60^\\circ)$ as $R\\cos(x - \\alpha)$, with $R > 0$ and $0^\\circ < \\alpha < 90^\\circ$. State $R$ exactly, and give $\\alpha$ correct to $2$ decimal places.
(b)[4]
Using this, solve the equation
$3\\cos 2\\theta + 2\\cos(2\\theta - 60^\\circ) = 2.5$
for $0^\\circ < \\theta < 180^\\circ$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “After expanding $\\cos(x-60^\\circ)$, arrive at $4\\cos x+\\sqrt3\\sin x$” …