Find the number of solutions for the equation `sin 5x+sin 3x+sin x=0` – InterviewSolution

1.	Find the number of solutions for the equation `sin 5x+sin 3x+sin x=0` for `0 le x le pi`.
Answer» Correct Answer - 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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