Number of solution(s) of the equation `(sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27x)=0` in the interval `(0,pi/4)` is____________

Answer

6

Explanation

`(sinx)/(cos3x) + (sin3x)/(cos9x) + (sin9x)/(cos27x) = 0`
`rArr (2sinxcosx)/(2cos3xcosx) + (2sin3xcos3x)/(2cos9xcos3x)`
`+(2sin9xcos9x)/(2cos27xcos9x) = 0`
`rArr (sin(3x-x))/(2cos3xcosx) + (sin(9x - 3x))/(2cos9xcos3x)`
`+(sin(27x - 9x))/(2cos27xcos9x) = 0`
`rArr (tan 3x - tanx) + (tan 9x - tan3x) + (tan27x - tan9x) = 0`
`rArr tan27x = tanx, 27x = npi + x, x = (npi)/(26) n in I`
`x = (pi)/(26), (2pi)/(26), (3pi)/(26), (4pi)/(26), (5pi)/(26), (6pi)/(26)`