Question

prove that cos A divide 1+sin A+1+sinA
by cos A=2secA

​

Answer 1

$\frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } + \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) } \\ \\ \frac{cos^{2} \alpha + {(1 + \sin( \alpha ) })^{2} }{ \cos( \alpha )( \sin( \alpha ) + 1 ) } \\ \\ {1 - sin^{2} \alpha } = cos^{2} \alpha \\ \\ \frac{(1 - sin^{2} \alpha ) + 1 + \sin^{2} \alpha + 2 \sin( \alpha ) }{ \cos( \alpha )(1 + \sin( \alpha )) } \\ \\ \frac{2(1 + \sin( \alpha ) )}{ \cos( \alpha ) (1 + \sin( \alpha )) } \\ \\ \frac{2}{ \cos( \alpha ) } \\ \\ and \: we \: know \: that \: \frac{1}{ \cos( \alpha ) } = \sec( \alpha ) \\ \\ 2 \sec( \alpha ) \\ \\ hence \: proved$