Question

cosec A + cot a is equal to one upon CosecA - cotA

Answer 1

CosecA + Cota = 1/(CosecA - CotA)

Simplify the eq
LHS
$\frac{1}{ {sin} \alpha } + \frac{ cos \alpha }{ {sin} \alpha } = \frac{1 + cos \alpha }{sin \alpha }$

RHS
$\frac{1}{ \frac{1}{sin \alpha } - \frac{cos \alpha }{sin \alpha } } = \frac{sin \alpha }{1 - cos \alpha }$
$\frac{ \sin \alpha(1 + \cos \alpha ) }{(1 - \cos\alpha ) (1 + \cos\alpha ) }$
$\frac{ { \sin \alpha } }{ {1 - cos}^{2} \alpha } (1 + \cos \alpha )$
$\frac{sin \alpha(1 + \cos\alpha ) }{ { \sin\alpha }^{2} }$
$\frac{1 + \cos \alpha }{ \sin\alpha }$
LHS = RHS