Find the general solution of each of the following equations:
cot x + tan x = 2 cosec x
To Find: General solution.
Given: cot x + tan x = 2 cosec x cos2x + sin2x = 2 sinx cosx cosec x 1 = sin 2x cosec x
cosec 2x = cosecx sin x = sin 2x sin x = 2 sin x cos x sin x = 0 or cos x = = cos()
Formula used: sin = 0 = n, cos = cos = 2n
By using above formula , we have
x = n or x = 2m where n, m I
So general solution is x = n or x = 2m where n, m I