Question

If 3x = cosec θ and `3/x = cot θ`, find the value of `3(x^2 - 1/x^2)`.

Answer 1

3 `(x^2 -1/x^2)`

`=9/3(x^2 - 1/x^2)`

=`1/3 (9x^2-9/x^2)`

=`1/3 [(3x^2)-(3/x)^2]`

=`1/3 [(cosec theta )^2 - (cot theta)^2]`

=`1/3 ( cosec^2 theta - cot^2 theta)`

=`1/3 (1)=1/3`