`sin x + sin 3x + sin 5x =0` को हल कीजिए |

Explanation

दिया है, `" " sin x + sin 3x + sin 5x = 0`
`rArr " " (sin 5x + sin x)+sin 3x=0`
`rArr " " "2 sin"(5x+x)/(2)"cos"(5x-x)/(2)+sin 3x =0`
`[because sin C + sin D = 2 sin((C+D)/(2))cos((C-D)/(2))]`
`rArr " " 2 sin 3 x cos 2x + sin 3x = 0`
` rArr " " sin 3x (2 cos 2x + 1)=0`
`" " sin 3x =0` या `2cos 2x + 1 =0`
जब `sin 3x = 0`, तब `" " 3x = n pi rArr x = (n pi)/(3)`.
तथा, जब `2 cos 2x + 1 =0`, तब `cos 2x = -(1)/(2)`
`rArr " " cos 2x =- "cos"(pi)/(3)`
`rArr " " cos 2x = cos(pi-(pi)/(3)) " " [because cos (pi-theta)=-cos theta]`
`rArr " " cos 2x = "cos"(2pi)/(3)`
`rArr " " x = 2n pi pm(2pi)/(3)`
`rArr " " x n pi pm (pi)/(3)`.