If `3x=cosectheta` and `3/x=cottheta` find the value of `3(x^2-1/x^2)`

Options

A. `(1)/(27)`
B. `(1)/(81)`
C. `(1)/(3)`
D. `(1)/(9)`

Answer

C

Explanation

We know that `" cosec"^(2)theta -cot^(2)theta=1.`
`therefore (3x)^(2)-((3)/(x))^(2)=1rArr9x^(2)-(9)/(x^(2))=1rArr9(x^(2)-(1)/(x^(2)))=1`
`rArr(x^(2)-(1)/(x^(2)))=(1)/(9)rArr3(x^(2)-(1)/(x^(2)))=3xx(1)/(9)=(1)/(3).`