Question

cosecA/cotA+tanA=cosA

Answer 1

cot A + tanA
= 1/sinA*cosA
coseca = 1/SinA
sinAcosA/sinA = cosA

Answer 2

Hi...☺

Here is your answer...✌

TO PROVE :

$\frac{ \cosec A }{ \cot A + \tan A } \: = \sin A$
PROOF :

LHS

$= \frac{ \cosec A }{ \cot A + \tan A } \\ \\ =\frac{ \cosec A }{ \frac{ \cos A }{ \sin A } + \frac{ \sin A }{ \cos A } } \\ \\ = \frac{ \cosec A}{ \frac{{ \cos}^{2} A + { \sin }^{2} A }{ \sin A \cos A} } \\ \\ = \frac{ \frac{1}{ \sin A} }{ \frac{1}{\sin A \cos A} } \: \: \: \: \: \: \: \: \: \: | \because \cosec A = \frac{1}{ \sin A} | \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |\because {\cos}^{2} A + { \sin }^{2} A = 1 | \\ \\ = \frac{\sin A \cos A}{ \sin A} \\ \\ = \cos A$

= RHS [Proved]