Question

√{(1+cos α°) /(1-cosα°)}=cot α/2°

Answer 1

hello users ......

we have to prove that ;
$\frac{ \sqrt{1 + cos \alpha } }{ \sqrt{ 1 - cos \alpha} }$ = cot $\frac{ \alpha }{2}$

solution :-
we know that 
1 + cos 2x = 2 cos² x 
and 
1 - cos 2x = 2 sin² x 

here

$\frac{ \sqrt{1 + cos \alpha } }{ \sqrt{ 1 - cos \alpha} }$ = $\frac{ \sqrt{2 cos^{2} \frac{ \alpha }{2} } }{ \sqrt{2 sin^{2} \frac{ \alpha }{2} } }$

=  √ cot² α/2
 = cot α/2 = RHS 

hence ;
√{(1+cos α°) /(1-cosα°)}=cot α/2° 

✪✪ hope it helps ✪✪