Question

prove that cotA/2+tanA/2=2cosecA​

Answer 1

Plz assume 'a' as 'A'

$\cot (\frac{a}{2} )+ \tan( \frac{a}{2} ) = \frac{ \ \ \cos ( \frac{a}{2} ) }{ \sin( \frac{a}{2} ) } + \frac{ \sin( \frac{a}{2} ) }{ \cos (\frac{a}{2}) }$

$\: \: \: \: \: = \frac{ \cos^{2} \frac{a}{2} + \sin^{2} \frac{a}{2} }{ \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) }$

$\: \: \: \: \: = \frac{1}{ \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) }$

$\: \: \: \: \: = \frac{2}{2} \times \frac{1}{ \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) }$

$\: \: \: \: \: = \frac{2}{2 \sin( \frac{a}{2} ) \cos( \frac{a}{2} ) }$

$\: \: \: \: \: = \frac{2}{ \sin2( \frac{a}{2} ) } \: \: \: \: \: \: \: \:( since \: 2 \sin(a ) \cos(a) = \sin2(a) )$

$\: \: \: \: \: = \frac{2}{ \sin(a) }$

$\: \: \: \: \: = 2 \ \cosec (a)$

Hence proved.plz give thanks for me