A deep-space communication laser's alignment angle ψ \psi\,ψ is modeled by the equation 6sinψcosψcosψ+sinψ=(5+sec2ψ)(cosψ−sinψ)\frac{6 \sin \psi \cos \psi}{\cos \psi + \sin \psi} = (5 + \sec 2\psi)(\cos \psi - \sin \psi)cosψ+sinψ6sinψcosψ=(5+sec2ψ)(cosψ−sinψ)
Show that this equation can be simplified to the form 6sin2ψ−10cos2ψ=26 \sin 2\psi - 10 \cos 2\psi = 26sin2ψ−10cos2ψ=2
For an observation window 0<t<π0 < t < \pi0<t<π, determine the values of the signal time t t\,t satisfying 6sintcostcost+sint=(5+sec2t)(cost−sint)\frac{6 \sin t \cos t}{\cos t + \sin t} = (5 + \sec 2t)(\cos t - \sin t)cost+sint6sintcost=(5+sec2t)(cost−sint) giving your answers to 3 significant figures.
Practise Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x with exam-style questions for A Level Maths. 19 questions, 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.