In an investigation of harmonic motion, a physicist requires the double-angle identities for an angle θ\thetaθ.
Starting with the identity for sin(A+B)\sin(A + B)sin(A+B), find an expression for sin2θ \sin 2\theta\,sin2θ in terms of sinθ \sin \theta\,sinθ and cosθ\cos \thetacosθ.
Starting with the identity for cos(A+B)\cos(A + B)cos(A+B), find an expression for cos2θ \cos 2\theta\,cos2θ in terms of sinθ \sin \theta\,sinθ and cosθ\cos \thetacosθ.
Use the result from part (b) to express cos2θ \cos 2\theta\,cos2θ as a function of cosθ \cos \theta\,cosθ only.
Use the result from part (b) to express cos2θ \cos 2\theta\,cos2θ as a function of sinθ \sin \theta\,sinθ only.
Derive the formula for tan2θ \tan 2\theta\,tan2θ in terms of tanθ \tan \theta\,tanθ using the expansion of tan(A+B)\tan(A + B)tan(A+B).
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
