Question

heeeeyyyyyyyyyy ❤


Prove that
(sin alpha +cos alpha) (tan alpha+cot alpha) =sec alpha + cosec alpha​

Answer 1

AnswEr :

• To Prove :

$( \sin( \alpha ) + \cos( \alpha) ) ( \tan( \alpha ) + \cot( \alpha )) = \sec( \alpha ) + \csc( \alpha )$

• Proof :

$\leadsto( \sin( \alpha ) + \cos( \alpha) ) ( \tan( \alpha ) + \cot( \alpha ))$

$\leadsto( \sin( \alpha ) + \cos( \alpha) ) \bigg( \dfrac{ \sin( \alpha ) }{ \cos( \alpha ) } + \dfrac{ \cos( \alpha ) }{ \sin( \alpha ) } \bigg)$

$\leadsto( \sin( \alpha ) + \cos( \alpha) ) \bigg( \dfrac{ \sin ^{2} ( \alpha ) + \cos^{2} ( \alpha ) }{ \cos( \alpha ) \sin( \alpha ) } \bigg)$

$\leadsto( \sin( \alpha ) + \cos( \alpha) ) \bigg( \dfrac{1}{ \cos( \alpha ) \sin( \alpha ) } \bigg)$

$\leadsto \dfrac{\sin( \alpha ) + \cos( \alpha) }{ \cos( \alpha ) \sin( \alpha ) }$

$\leadsto \dfrac{ \cancel{\sin( \alpha )}}{ \cos( \alpha ) \cancel{\sin( \alpha )}} + \dfrac{\cancel{\cos( \alpha )}}{ \cancel{\cos( \alpha )} \sin( \alpha ) }$

$\leadsto \dfrac{1}{ \cos( \alpha ) } + \dfrac{1}{ \sin( \alpha ) }$

$\leadsto \large{\sec( \alpha ) + \csc( \alpha ) }$

⠀

$\therefore \boxed{ \sin( \alpha ) + \cos( \alpha) ) ( \tan( \alpha ) + \cot( \alpha )) = \sec( \alpha ) + \csc( \alpha ) }$

Answer 2

Hope this helps you ......