Question

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

Answer 1

`cot x = -5/3 -> tan x = -3/5`. Call tan x = t

`Use the trig identity: cos 2x = (1 - t^2)/(1 + t^2)`
`cos 2x = -(1 - 9/25)/(1 + 9/25) = -16/34 = -8/17`