Question

General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.

Options

• `(nπ)/4 or nπ ± π/6`

• `nπ or nπ ± π/3`

• `nπ ± π/4`

• `nπ or 2nπ ± π/4`

Answer 1

General solution of the equation sin 2x – sin 4x + sin 6x = 0 is `underlinebb((nπ)/4 or nπ ± π/6)`.

Explanation:

sin 2x – sin 4x + sin 6x = 0

`\implies` (sin 2x + sin 6x) – sin 4x = 0

`\implies` 2 sin 4x cos 2x – sin 4x = 0

sin 4x = 0 `\implies` 4x = nπ  `\implies` x = `π/4`

2 cos 2x – 1 = 0 `\implies` cos 2x = `1/2`

`\implies` 2x = `2nπ ± π/3 or x = nπ ± π/6`