Math, asked by iamprincesingh, 1 year ago

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

Answers

Answered by sandy1816
4

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

Answered by umiko28
11

\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}

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