Question

show that -->
$cos \: a \: \sqrt{1 + cot { }^{2} }a \: \: \: = \: \: \sqrt{cosec { \: }^{2} } a \: - 1 \:$

Answer 1

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