A sub-aquatic drone's descent angle θ \theta\,θ is controlled by a buoyancy system. To maintain stable movement, the angle must satisfy the equilibrium equation:
5cot2θ+3 cosec2θ=2 cosec θ+105\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 105cot2θ+3 cosec2θ=2 cosec θ+10
Show that this equation can be written in the form a cosec2θ+b cosec θ+c=0a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0a cosec2θ+b cosec θ+c=0 where aaa, bbb, and c c\,c are integers to be found.
Hence, given that the drone is tilted at an obtuse angle θ \theta\,θ that satisfies this stability equation, determine the exact value of tanθ\tan \thetatanθ. Fully justify your answer.
Practise Edexcel A Level Maths 6.4 Trigonometric Identities with exam-style questions for A Level Maths. 12 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.