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Find the number of solutions for the equ...

Find the number of solutions for the equation `sin 5x+sin 3x+sin x=0` for `0 le x le pi`.

Text Solution

Verified by Experts

The correct Answer is:
Three solutions
`sin 3x + (sin 5x + sin x) = 0`
`rArr sin 3x + (2 sin 3x cos 2x) = 0`
`rArr sin 3x = 0`
or `cos 2x = -(1)/(2) = "cos"(2pi)/(3), n in Z`
`rArr x = npi//3`
or `x = 2n pi -+ (2pi)/(3)`
Then `x = 0, pi//3, 2pi//3`,
Hence, there are three solutions
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