Question

simplify .............

Answer 1

hey buddy here's ur answer

Answer 2

$\sin( \beta ) \bigg[ \frac{ \cos( \beta ) + \sin( \beta ) }{ \cos( \beta ) } \bigg] + \cos( \beta ) \bigg[ \frac{ \sin( \beta ) + \cos ( \beta ) }{ \sin( \beta ) } \bigg] \\ \\ = \sin( \beta ) \bigg[ \frac{ \sin( \beta ) + \cos ( \beta )}{ \cos( \beta ) } \bigg] + \cos( \beta ) \bigg[ \frac{ \sin( \beta ) + \cos ( \beta ) }{ \sin( \beta ) } \bigg] \\ \\ = \frac{\sin( \beta )[\sin( \beta ) + \cos ( \beta )]}{ \cos( \beta ) } + \frac{ \cos( \beta )[ \sin( \beta ) + \cos ( \beta )] }{ \sin( \beta ) } \\ \\ \text{Take \big(\sin( \beta ) + \cos ( \beta ) \big) common}\\ \\ =\big(\sin( \beta ) + \cos ( \beta ) \big) \bigg( \frac{ \sin( \beta ) }{ \cos( \beta ) } + \frac{ \cos( \beta ) }{ \sin( \beta ) } \bigg)$


$= \big(\sin ( \beta ) + \cos ( \beta ) \big) \bigg( \frac{ \sin ^{2} ( \beta ) + \cos ^{2} ( \beta ) }{ \sin( \beta ) \cos( \beta ) } \bigg) \\ \\ =\big(\sin ( \beta ) + \cos ( \beta ) \big) \bigg( \frac{1 }{ \sin( \beta ) \cos( \beta ) } \bigg) \\ \\ = \frac{\sin ( \beta ) + \cos ( \beta )}{ \sin( \beta ) \cos( \beta ) } \\ \\ = \frac{ \sin( \beta ) }{ \sin( \beta ) \cos( \beta ) } + \frac{ \cos( \beta ) }{ \sin( \beta ) \cos( \beta ) } \\ \\ = \frac{1}{ \cos( \beta ) } + \frac{1}{ \sin( \beta ) } \\ \\ = \sec( \beta ) + \cosec( \beta )$