A student is asked to derive several double-angle identities for a classroom presentation using the compound angle formulae.
By substituting B=xB = xB=x into the addition formula for sin(x+B)\sin(x + B)sin(x+B), show that sin2x=2sinxcosx\sin 2x = 2 \sin x \cos xsin2x=2sinxcosx.
Using the identity for cos(A+B)\cos(A + B)cos(A+B), derive an expression for cos2x \cos 2x\,cos2x in terms of sinx \sin x\,sinx and cosx\cos xcosx.
Hence, show that cos2x=2cos2x−1\cos 2x = 2 \cos^2 x - 1cos2x=2cos2x−1.
Hence, show that cos2x=1−2sin2x\cos 2x = 1 - 2 \sin^2 xcos2x=1−2sin2x.
Use the formula for tan(A+B)\tan(A + B)tan(A+B) to derive the identity for tan2x \tan 2x\,tan2x in terms of tanx\tan xtanx.
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.
