Find the general solutions of the following equations :

tan mx + cot nx = 0

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,

⇒

We know that: cot θ = tan (π/2 – θ)

∴

⇒ { ∵ - tan θ = tan -θ }

If tan x = tan y, then x is given by x = kπ + y, where k ∈ Z.

From above expression, on comparison with standard equation we have

y =

∴

⇒

,where k ϵ Z …ans