Question

1-1/sin square theta

Answer 1

Given,

$\[1 - \frac{1}{{{{\sin }^2}\theta }}\]$

Solution,

$\[ = 1 - \frac{1}{{{{\sin }^2}\theta }}\]$

$\[ = 1 - \frac{{\left( {{{\sin }^2}\theta + {{\cos }^2}\theta } \right)}}{{{{\sin }^2}\theta }}\]$

$\[ = 1 - \left( {1 + {{\cot }^2}\theta } \right)\]$

$\[ = - {\cot ^2}\theta \]$

Hence the value is $\[ - {\cot ^2}\theta \]$.