Q. 4 F5.0( 1 Vote )

# Solve the followi

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,

sin x + sin 2x + sin 3x = 0

To solve the equation we need to change its form so that we can equate the t-ratios individually.

For this we will be applying transformation formulae. While applying the

Transformation formula we need to select the terms wisely which we want

to transform.

As, sin x + sin 2x + sin 3x = 0

we will use sin x and sin 3x for transformation as after transformation it will give sin 2x term which can be taken common.

{ sin A + sin B = sin 2x + 2 sin 2sin 2x cos x + sin 2x = 0

sin 2x ( 2cos x + 1) = 0

either, sin 2x = 0 or 2cos x + 1 = 0

sin 2x = sin 0 or cos x = - � = cos (π-π/3) = cos 2π/3

If sin x = sin y, implies x = nπ + (– 1)ny, where n Z.

If cos x = cos y, implies x = 2nπ ± y, where n Z.

Comparing obtained equation with standard equation, we have:

2x = nπ or x = 2mπ ± 2π/3 where m,n ϵ Z ..ans

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