Ideas required to solve the problem:
The general solution of any trigonometric equation is given as –
• sin x = sin y, implies x = nπ + (– 1)ny, where n ∈ Z.
• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
• tan x = tan y, implies x = nπ + y, where n ∈ Z.
given,
cot x + tan x = 2
⇒ ( tan x – 1 )2 = 0
∴ tan x = 1 ⇒ tan x = tan \(\frac{π}4\)
If tan x = tan y, implies x = nπ + y, where n ∈ Z.
∴ x = nπ + \(\frac{π}4\) where n ϵ Z ….ans