Question

How do you use find the exact value of cos2x, given that cotx = -5/3 with pi/2<x<pi?

Answer 1

`8/17`

Explanation:

Use trig identity:
`sin^2 x = 1/(1 + cot^2 x)`
In this case:
`sin^2 x = 1/(1 + 25/9) = 9/34`
Apply trig identity:
`cos 2x = 1 - 2sin^2 x`
In this case:
`cos 2x = 1 - 18/34 = 16/34 = 8/17`