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The solution of sin x + sin5x = sin 3x i...

The solution of sin x + sin5x = sin 3x in `(0,(pi)/(2))`

A

`(pi)/(4),(pi)/(10)`

B

`(pi)/(6),(pi)/(3)`

C

`(pi)/(4),(pi)/(2)`

D

`(pi)/(8),(pi)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `sinx+sin5x=sin3x`
`rArr2sin3xcos2x=sin3x`
`rArrsin3x(2cos2x-1)=0`
`rArrsin3x=0`
or `2cos2x-1=0`
`rArr3x=,pior 2x=(pi)/(3)`
`rArrx=0,x=(pi)/(3)orx=(pi)/(6)`
Hence , solutions are `(pi)/(3),(pi)/(6)`.
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