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+10 5\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 10 5cot2θ+3 cosec2θ=2 cosec θ+10Show that this equation can be written in the form
a cosec2θ+b cosec θ+c=0 a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0 a cosec2θ+b cosec θ+c=0where 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 AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) 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.
