Question

How do you find cos 2x, given cot x = 3/5 and csc x < 0?

Answer 1

`- 8/17`

Explanation:

`cos x / sin x = 3/5`

`(1 - sin^2 x) / sin^2 x = 9/25`

`9 sin^2 x = 25 - 25 sin^2 x`

`sin x = ± sqrt{ 25/34}`

`1/sin x < 0 Rightarrow sin x = - 5/ sqrt 34`

`cos 2x = (1 - sin^2 x) - sin^2 x = 1 - 2 * 25 / 34`