Q. 2 I

# Find the general solutions of the following equations :

tan px = cot qx

Answer :

**Ideas required to solve the problem:**

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)^{n}y, 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)

∴

If tan x = tan y, then x is given by x = nπ + y, where n ∈ Z.

From above expression, on comparison with standard equation we have

y =

∴

⇒

∴ **,where n** **ϵ** **Z**

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