The number of solutions of `"cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c^(-1)x))))+1=0` where `x >0` is

Answer

3

Explanation

`cos (2 sin^(-1) (cot (tan^(-1) (sec(6 cosec^(-1) x))))) = -1`
`rArr sin^(-1) (cot (tan^(-1) (sec (6 cosec^(-1) x)))) = +- (pi)/(2)`
`rArr cot (tan^(-1) (sec(6 cosec^(-1) x))) = +-1`
`rArr tan^(-1) (sec(6 cosec^(-1) x)) = (pi)/(4), (3pi)/(4)`
`rArr sec(6 cosec^(-1) x) = +-1`
`rArr 6 cosec^(-1) x = +- 3pi, 2pi, +- pi`
`rArr cosec^(-1) x = +- (pi)/(2), +- (pi)/(3), +- (pi)/(6)`
`rArr x = 1, (2)/(sqrt3) , 2 " " ( :' x gt 0)`