Question

Trigonometry question proof

Answer 1

Answer: 2

Explanation:

We can manipulate the left-hand side as follows.

`\tan \theta+\cot \theta\\\\=(\sin \theta)/(\cos \theta)+(\cos \theta)/(\sin \theta)\\\\=(\sin^(2) \theta+\cos^(2) \theta)/(\cos \theta \sin \theta)\\\\=(1)/(\cos \theta \sin \theta)\\\\=(1)/((1)/(2) sin 2\theta)\\\\=\boxed{2} \text{ cosec} 2\theta`