Solve the following equations :

cot x + tan x = 2

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 π/4

If tan x = tan y, implies x = nπ + y, where n ∈ Z.

∴ x = nπ + π/4 where n ϵ Z ….ans