Question

If `cosec  theta = 2x and cot theta = 2/x ," find the value of"  2 ( x^2 - 1/ (x^2))`

Answer 1

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

=`4/2(x^2 - 1/(x^2))`

=`1/2(4x^2 - 4/(x^2))`

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

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

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

=`1/2 (1)`

=`1/2`