Question

please helpp
Solve the equation tan 2x = 5 cot x, for 0< x < 180

Answer 1

I suggest you change this to an equation in tan x using the identities

tan 2x = 2 tan x / (1 - tan^2 x)
and
cot x = 1/ tan x

Answer 2

okay

Answer 3

so we get
2 tan x = 5
------- --
1 - tan^ x tan x

Answer 4

cross multiply
2 tan ^2 x = 5 - 5 tan^2 x

now its easy

Answer 5

just add 5 tan^2 x to both sides
then divide both sides by 7
to give a value for tan^2 x
and take the square roots