Question

Calculate the value of cot2teta-1/sin2teeta

Answer 1

${ \cot}^{2} \beta - \frac{1}{ { \sin}^{2} \beta } \\ \\ = { \cot}^{2} \beta - { \cosec }^{2} \beta \\ \\ = - ({ \cosec }^{2} \beta - { \cot}^{2} \beta ) \\ \\ = - 1$