Question

Find the general solution of cot x + tan x = 2 cosesc x.

Answer 1

cot x + tan x = 2 cosesc x

`cosx/sinx+sinx/cosx=2/sinx`

`(cos^2x+sin^2x)/(sinx.cosx)=2/sinx`

`1/(sinx.cosx)=2/sinx` ...................[`because cos^2x+sin^2x=1`]

`1=2/sinx xx sinx.cosx`

`1=2cosx`

`cosx=1/2`

`x=cos^-1(1/2)=pi/3`

Since, cos θ= cos α implies `theta=2npi+-alpha,n in Z`

the required general solution is `x=2npi+-pi/3` where `n in Z`