Q. 2 K5.0( 1 Vote )

# Find the general solutions of the following equations :

sin x = tan x

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,

⇒

⇒

⇒

either,

sin x = 0 or cos x = 1

⇒ sin x = sin 0 or cos x = cos 0

We know that,

If sin x = sin y, implies x = nπ + (– 1)^{n} y, where n ∈ Z

∵ sin x = sin 0

∴ y = 0

And hence,

**x = n**π **where n** **ϵ** **Z**

Also,

If cos x = cos y, implies x = 2mπ ±y, where m ∈ Z

∵ cos x = cos 0

∴ y = 0

Hence, x is given by

**x = 2m**π **where m** **ϵ** **Z**

**∴** **x = n**π **or 2m**π **,where m,n** **ϵ** **Z …ans**

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