Question

How do you use the double angle or half angle formulas to solve `tan2x-cotx=0`?

Answer 1

Solve tan 2x - cot x = 0

Ans: `pi/6 and (5pi)/6`

Explanation:

Use trig identity: `tan 2x = (2tan x)/(1 - tan^2 x)`
Call tan x = t, we get:
`(2t)/(1 - t^2) - 1/t = 0`
`(2t^2 - 1 + t^2)/(t(1 - t^2)) = 0`
`3t^2 = 1` --> `t^2 = 1/3` -->`t = +- sqrt3/3`.
a.`t = tan x = sqrt3/3` --> `x = pi/6` , or `60^@`
b. `tan x = -sqrt3/3` --> `x = (5pi)/6` or `150^@`