Number of solutions of the equation `cos 5x xx tan (6|x|)+sin 5x=0` lying in `[-2pi, pi)` is _____.

Answer

13

Explanation

We have `cos 5x xx tan 6|x|+ sin5x=0`
Case I :
`x ge 0`
`:. Cos 5x tan 6x + sin 5x =0`
`rArr cos 5x sin 6x+ sin 5x cos 6x =0`
`rArr sin 11x=0`
`rArr 11x=n pi`
`rArr x= (npi)/11, n in Z^(+) uu {0}`
So, there will be eleven solutions for `n=0, 1, 1, ..., 10`.
Case II :
`x lt 0`
`:. -cos 5x tan 6x + sin 5x=0`
`rArr -cos 5x sin 6x+ cos 6x sin 5x =0`
`rArr sin(5x-6x)=0`
`rArr sin x=0`
`rArr x=npi, N in Z`
`:. x=-pi, -2pi`
So, total number of solution is 13.