A sub-aquatic drone's descent angle $\theta\,$ is controlled by a buoyancy system. To maintain stable movement, the angle must satisfy the equilibrium equation:

5\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 10

Show that this equation can be written in the form

a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0

where $a$ , $b$ , and $c\,$ are integers to be found.

Hence, given that the drone is tilted at an obtuse angle $\theta\,$ that satisfies this stability equation, determine the exact value of $tan⁡θ\tan \theta$ . Fully justify your answer.

A sub-aquatic drone's descent angle $\theta\,$ is controlled by a buoyancy system. To maintain stable movement, the angle must satisfy the equilibrium equation:

5\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 10

Show that this equation can be written in the form

a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0

where $a$ , $b$ , and $c\,$ are integers to be found.

Hence, given that the drone is tilted at an obtuse angle $\theta\,$ that satisfies this stability equation, determine the exact value of $tan⁡θ\tan \theta$ . Fully justify your answer.

1 Unit 1: Pure Mathematics A

Question 269

Markscheme

1 Unit 1: Pure Mathematics A

Question 269

Markscheme

1 Unit 1: Pure Mathematics A

Question 269

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 269

1 Unit 1: Pure Mathematics A Questions