A-level · Trigonometry

Addition formulaeExam-style questions

The compound-angle formulae for sin(A±B), cos(A±B) and tan(A±B) — the sign patterns to get right, and using them for exact values of non-standard angles, expanding, proving identities and solving equations.

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

DifficultyAll Level 3 Level 4 Level 5

1
Use an addition formula to find the exact value of $\sin 75^\circ$ .
Level 3 · 3 marksTry it
2
Use an addition formula to show that $\tan 75^\circ = 2 + \sqrt{3}$ .
Level 3 · 3 marksTry it
3
$A$ and $B$ are acute angles with $\sin A = \frac{3}{5}$ and $\cos B = \frac{5}{13}$ . Find the exact values of (a) $\sin(A+B)$ ,
(b) $\cos(A+B)$ .
Level 3 · 4 marksTry it
4
Prove that $\cos(A-B) - \cos(A+B) \equiv 2\sin A\sin B$ .
Level 3 · 2 marksTry it
5
Solve $\cos(x + 30^\circ) = \sin x$ for $0 \le x \le 360^\circ$ .
Level 3 · 4 marksTry it

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