Question

please anybody answer this question​

Answer 1

$\large \bold \blue{ \underline{answer}} \\ \large \bold{a \: \: lies \: \: in \: \: 1st \: \: and \: \: 2nd \: \: quadrant}$

Step-by-step explanation:

$\large \bold \green{ \underline{to \: \: find}} \\ \text{a lies \: in \: which \: quadrant} \\ \large \bold \pink{ \underline{explanation}} \\ \implies\sqrt{ \frac{1 + \cos(a) }{1 - \cos(a) } } \\ \implies{ \sqrt{ \frac{1 + \cos(a) }{1 - \cos(a) } } } \times \sqrt{ \frac{1 + \cos(a) }{1 + \cos(a) } } \\ \implies{ \sqrt{ \frac{(1 + \cos(a) ) {}^{2} }{ \sin {}^{2}a } } } \\ \implies{ \sqrt{ (\csc(a) + \cot(a)) {}^{2} } } \\ \implies | \csc(a) + \cot(a) | {} \\ \implies{ \csc(a) + \cot(a) = \: given } \\ \implies{let \: \: \csc(a) + \cot(a) = x } \\ \implies{ |x| = x } \\ \implies{it \: \: is \: \: possible \: \: when \: \: x \geqslant 0} \\ \implies{ \csc(a) + \cot(a) \geqslant 0 } \\ \implies{it \: \: \: means \: \: that \: \: \sin(x) > 0 } \\ \implies{it \: \: is \: \: possible \: \: only \: \: in \: \: 1st \: \: and \: \: 2 nd\: \: quadrant} \\ \implies \therefore \green{a \: \: lies \: \: in \: \: 1st \: \: and \: \: 2nd \: \: quadrant}$