The angle of rotation ψ\psiψ of a high-precision robotic arm, where 0<ψ<π0 < \psi < \pi0<ψ<π, is determined by the following equilibrium equation:
4cot2ψ+2=4cscψ+134\cot^2 \psi + 2 = 4\csc \psi + 134cot2ψ+2=4cscψ+13
Show that the equation can be written in the form acsc2ψ+bcscψ+c=0a\csc^2 \psi + b\csc \psi + c = 0acsc2ψ+bcscψ+c=0 where aaa, bbb, and ccc are integers to be found.
Hence, given that the robotic arm is positioned at an obtuse angle ψ\psiψ that satisfies the original equation, find the exact value of tanψ\tan \psitanψ. Fully justify your answer.
Practise Edexcel A Level Maths Trigonometric Functions with exam-style questions for A Level Maths. 36 questions covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse 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.