If solution of `cot(sin^(-1)sqrt(1-x^(2)))=sin(tan^(-1)(xsqrt(6))),x!=0` is `1/psqrt(q/r)` where `p,q,r` are prime then value of `(p+q-r)/p` is

Answer

2

Explanation

`cot(sin^(-1)sqrt(1-x^(2)))`
`x/(sqrt(1-x^(2))`
`sin(tan^(-1)xsqrt(6))=(xsqrt(6))/(sqrt(6x^(2)+1))`
`implies(sqrt(6))/(sqrt(6x^(2)+1))=1/(sqrt(1-x^(2)))implies12x^(2)=5`
`impliesx=+-1/2sqrt(5/3)`
so `x=1/2sqrt(5/3)`
(but `x` will be positive
`impliesp=2, q=5, r=3`
So `(p+q-r)/p=(2+5-3)/2=2`