Q. 2 K5.0( 1 Vote )

# Find the general solutions of the following equations :sin x = tan x

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 = nπ 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 = 2mπ where m ϵ Z

x = nπ or 2mπ ,where m,n ϵ Z …ans

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