Question

plz. solve this question

Answer 1

Ok.......................

Answer 2

$\sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \\ \tan( \alpha ) = \frac{1}{\sqrt{3} } \\ \\ \tan( \alpha ) = \tan(30) \\ \\ \alpha = 30$

Now,

$\frac{ \sin( \alpha ) \times \ \tan ( \alpha ) \times (1 + \cot( \alpha )) }{ \sin( \alpha ) + \cos( \alpha ) } \\ \\ = \frac{ \sin(30) \times \tan(30) \times (1 + \cot(30)) }{ \sin(30) + \cos(30) } \\ \\ = \frac{ \frac{1}{2} \times \frac{1}{ \sqrt{3} } \times (1 + \sqrt{3}) }{ \frac{1}{2} + \frac{ \sqrt{3} }{2} } \\ \\ = \frac{( \frac{1 + \sqrt{3} }{2 \sqrt{3} } )}{ \frac{(1 + \sqrt{3}) }{2} } \\ \\ = \frac{1}{ \sqrt{3} }$