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The solution of sinx+sin5x=sin3x in (0,(...

The solution of `sinx+sin5x=sin3x` 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:
D
Given `sinx=sin 5x=sin 3x`
`=2sin 3xcos 2x=sin 3x`
`impliessin 3x(2 cos 2x-1)=0`
`impliessin 3x=0` ltborgt `2cos 2x-1=0`
`implies3x=0, pi` ro `2x=(pi)/3`
`impliesx=0, x=(pi)/3` or `x=(pi)/6`
`:.` Solutions in `(0,(pi)/2)` are `(pi)/3,(pi)/6`.
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