Question

find
sin60 / 1- cos60 + cos60 / 1-sin60

​

Answer 1

$\frac{ \sin( \alpha ) }{1 - \cos( \alpha ) } + \frac{ \cos( \alpha ) }{1 - \sin( \alpha ) }$

$\frac{ \sin( \alpha )(1 + \cos( \alpha ) ) }{1 - { \cos( \alpha ) }^{2} } + \frac{ \cos( \alpha ) (1 + \sin( \alpha ) )}{1 - { \sin( \alpha ) }^{2} }$

$\frac{ \sin( \alpha ) (1 + \cos( \alpha ) )}{ { \sin( \alpha ) }^{2} } + \frac{ \cos( \alpha ) (1 + \sin( \alpha ) )}{ { \cos( \alpha ) }^{2} }$

$\frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } + \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) }$

$1 + \tan( \alpha ) + 1 + \cot( \alpha )$

$2 + \tan( \alpha ) + \cot( \alpha )$

Now, we know, if

$\alpha = 60 \: degree$

then,

$\tan( \alpha ) = \sqrt{3} = \frac{3}{ \sqrt{3} }$

$\cot( \alpha ) = \frac{1}{ \sqrt{3} }$

so,

$2 + \tan( \alpha ) + \cot( \alpha )$

$2 + \frac{3}{ \sqrt{3} } + \frac{1}{ \sqrt{3} }$

$2 + \frac{4}{ \sqrt{3} }$

$2 + \frac{4 \sqrt{3} }{3}$

so, putting

$\sqrt{3} = 1.732$

we get,

$2 + \frac{4 \times 1.732}{3}$

$2 + 4 \times 0.544$

$2 + 2.176$

$4.176 \: {approx}$

Hope this helps you...