A-level · Trigonometry

Double-angle formulaeExam-style questions

The double-angle formulae for sin 2A, cos 2A (three forms) and tan 2A, where they come from, choosing the right form of cos 2A, and using them to solve equations and find exact values.

Start practising Read the lesson

23 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
Given that $\sin\theta = \frac{3}{5}$ and $\theta$ is acute, find the exact values of (a) $\sin 2\theta$ ,
(b) $\cos 2\theta$ ,
(c) $\tan 2\theta$ .
Level 3 · 4 marksTry it
2
Prove that $\dfrac{\sin 2\theta}{1 + \cos 2\theta} \equiv \tan\theta$ .
Level 3 · 2 marksTry it
3
Solve $\sin 2x = \sin x$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 3 marksTry it
4
Solve $\cos 2x = \cos x$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 4 marksTry it
5
Solve $\cos 2x + \cos x + 1 = 0$ for $0 \le x \le 2\pi$ , giving your answers as exact multiples of $\pi$ .
Level 3 · 4 marksTry it

18 more questions on double-angle formulae

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free