Question

prove : cos A cot A/1-sin A=1+cosec A​

Answer 1

Answer:

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Answer 2

AnswEr :

• To Prove :

$\dfrac{ \cos( \alpha ) \cot( \alpha ) }{1 - \sin( \alpha ) } = 1 + \csc( \alpha )$

• Proof :

$\longrightarrow \dfrac{ \cos( \alpha ) \cot( \alpha ) }{1 - \sin( \alpha ) }$

$\longrightarrow \dfrac{ \cos( \alpha ) \times \dfrac{\cos( \alpha ) }{ \sin( \alpha ) } }{1 - \sin( \alpha ) }$

$\longrightarrow \dfrac{ \dfrac{\cos^{2} ( \alpha ) }{ \sin( \alpha ) } }{1 - \sin( \alpha ) }$

$\longrightarrow \dfrac{ { \cos}^{2} (\alpha )}{ \sin( \alpha ) } \times \dfrac{1}{ (1 - \sin( \alpha )) }$

$\longrightarrow \dfrac{1 - \sin^{2} ( \alpha ) }{ \sin( \alpha )(1 - \sin( \alpha )) }$

$\longrightarrow \dfrac{(1 + \sin( \alpha ) ) \cancel{(1 - \sin ( \alpha ) )}}{ \sin( \alpha ) \cancel{(1 - \sin( \alpha ))} }$

$\longrightarrow \dfrac{(1 + \sin( \alpha ) )}{ \sin( \alpha ) }$

$\longrightarrow \dfrac{1}{ \sin( \alpha ) } + \cancel\dfrac{ \sin( \alpha ) }{ \sin( \alpha ) }$

$\longrightarrow \csc( \alpha ) + 1$

$\longrightarrow 1 + \csc( \alpha )$