Question

$\sqrt{cosec ^{2} } theta \: - 1 \div cosec \: theta$
find the value of this ​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{ \cosec^{2} x - 1} }{ \cosec \: x } \\ = \frac{ \sqrt{1 + { \cot }^{2}x - 1 } }{ \cosec \: x} \\ = \frac{ \sqrt{ { \cot }^{2}x } }{ \cosec \: x} \\ = \frac{ \cot \: x }{ \cosec \: x } \\ = \frac{ \frac{ \cos(x) }{ \sin(x) } }{ \frac{1}{ \sin(x) } } \\ = \cos(x)$