By writing cos3ϕ \cos 3\phi\,cos3ϕ as cos(2ϕ+ϕ)\cos(2\phi + \phi)cos(2ϕ+ϕ), show that cos3ϕ=4cos3ϕ−3cosϕ\cos 3\phi = 4\cos^3 \phi - 3\cos \phicos3ϕ=4cos3ϕ−3cosϕ.
Solve, for 0≤ϕ≤1800 \leq \phi \leq 1800≤ϕ≤180, the equation,
12cos3ϕ−9cosϕ=1.5 12\cos^3 \phi - 9\cos \phi = 1.5 12cos3ϕ−9cosϕ=1.5Give your answers to 1 decimal place where necessary.
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.