Question

sinA by 1 + cosA is equals to cosecA - cotA​

Answer 1

Step-by-step explanation:

sinA/1+cosA

=sinA(1-cosA)/(1+cosA)(1-cosA)

=sinA(1-cosA)/1-cos²A

=sinA(1-cosA)/sin²A

=(1-cosA)/sinA

=cosecA-cotA

Answer 2

$\huge\mathbb{QUESTION \to: }$

sinA/(1 + cosA) =cosecA - cotA

$\huge\mathbb{SOLUTION \to: } \\ \\ \sf\ \frac{sinA}{1 + cosA} \\ \\ \tt\ \implies: \frac{sinA(1 - cosA)}{(1 + cosA)(1 - cosA)} \\ \\ \sf\ \implies: \frac{sinA(1 - cosA)}{( {1}^{2} - {cos}^{2}A )} \\ \\ \bf\ \implies: \frac{sinA(1 - cosA)}{( 1 - {cos}^{2}A )} \\ \\ \sf\ \implies: \frac{sinA(1 - cosA)}{ {sinA}^{2} } \\ \\ \sf\ \implies: \frac{(1 - cosA)}{ sinA } \\ \\ \bf\ \implies: \frac{1}{sinA} - \frac{cosA}{sinA} \\ \\ \sf\boxed{ \implies \: \sf \: cosecA - cotA \: \: \: \: \ddot \smile}$