Show that cotθ−tanθcotθ+tanθ≡cos2θ\frac{\cot \theta - \tan \theta}{\cot \theta + \tan \theta} \equiv \cos 2\thetacotθ+tanθcotθ−tanθ≡cos2θ for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ where n∈Zn \in \mathbb{Z}n∈Z.
The power output PPP (in Watts) of a specific AC circuit component is modelled by the function P(t)=11cos2(2t−40∘)P(t) = 11 \cos^2(2t - 40^\circ)P(t)=11cos2(2t−40∘), where ttt is a phase angle measured in degrees and 0∘≤t<90∘0^\circ \le t < 90^\circ0∘≤t<90∘.
Determine the values of ttt for which the power output is exactly 333 Watts, giving your answers to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)
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.