Question

${\huge{\underline{\underline{\bf{Question:-}}}}}$

if
$\frac{sin \: a}{1 - cot \: a} + \: \frac{cos \: a}{(1 - tan \: a)} =$
​

Answer 1

${\huge{\underline{\underline{\bf{Question:-}}}}}$

if

$\dfrac{sin \: a}{1 - cot \: a} + \: \dfrac{cos \: a}{(1 - tan \: a)} =$=?

$\Huge\mathtt\purple{an{\mathcal{S}}wer:}$

➔$\dfrac{sin \: a}{1 - \dfrac{cos \: a}{sin \: a} } + \: \dfrac{cos \: a}{1 - \dfrac{sin \: a}{cos \: a} }$

➔$\dfrac{ {sin}^{2}a }{(sin \: a - cos \: a)} + \dfrac{ {cos}^{2}a }{(cos \: a \: - sin \: a)}$

➔$\dfrac{ {sin}^{2} a}{(sin \: a \: - cos \: a)} - \: \dfrac{ {cos}^{2}a }{(sin \: a - \: cos \: a)}$

➔$\dfrac{ {sin}^{2} a - {cos}^{2} a}{(sin \: a \: - \: cos \: a)} = (sin \: a \: + \: cos \: a)$

$\huge\mathfrak\red{Thanks}$