Use the identity for sin(A+B)\sin(A + B)sin(A+B) to express sinAcosA \sin A \cos A\,sinAcosA in terms of sin2A\sin 2Asin2A.
Use the identity for cos(A+B)\cos(A + B)cos(A+B) to express cos2A−sin2A\cos^2 A - \sin^2 Acos2A−sin2A in terms of cos2A\cos 2Acos2A.
Hence, express cos2A \cos^2 A\,cos2A in terms of cos2A\cos 2Acos2A.
Hence, express sin2A \sin^2 A\,sin2A in terms of cos2A\cos 2Acos2A.
Use the identity for tan(A+B)\tan(A + B)tan(A+B) to express tan2A(1−tan2A)\tan 2A(1 - \tan^2 A)tan2A(1−tan2A) in terms of tanA\tan AtanA.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.