Question

prove the following​

Answer 1

Step-by-step explanation:

To prove: {cosec(A)+cot(A)}(1-cos(A))=sin(A)

Proof: Let us put α=A, so we get,

$( \csc( \alpha ) + \cot( \alpha ) )(1 - \cos( \alpha ) )$

$= ( \frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } )(1 - \cos( \alpha ) )$

$= ( \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } )(1 - \cos( \alpha ) )$

$= \frac{(1 + \cos( \alpha ))(1 - \cos( \alpha ) )}{ \sin( \alpha )}$

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

$= \frac{ \sin^{2} ( \alpha ) }{ \sin( \alpha ) }$

$= \sin( \alpha )$

Since, α=A, so

The requred answer is sin(A)

Hence, proved