Show that
cotθ−tanθcotθ+tanθ≡cos2θ \frac{\cot \theta - \tan \theta}{\cot \theta + \tan \theta} \equiv \cos 2\theta cotθ+tanθcotθ−tanθ≡cos2θfor 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.)
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.