Question 1114877
({{{sin(2b))/(1-cos(2b))=1/(tan(b))}}} 


start with left side and prove it is equal to right side:


{{{(sin(2b))/(1-cos(2b))}}}.....since  {{{sin(2b)=2sin(b)cos(b) }}},and {{{cos(2b) = cos^2(b) - sin^2(b) = 1 -2 sin^2(b) = 2 cos^2(b) - 1}}}, we have


={{{(2sin(b)cos(b))/(1-(2 cos^2(b) - 1))}}}


={{{(2sin(b)cos(b))/(1-2 cos^2(b) +1)}}}


={{{(2sin(b)cos(b))/(2-2 cos^2(b) )}}}


={{{(2sin(b)cos(b))/2(1-cos^2(b) )}}}


={{{(cross(2)sin(b)cos(b))/cross(2)(1-cos^2(b) )}}}


={{{(sin(b)cos(b))/(1-cos^2(b) )}}}.....since {{{1-cos^2(b)= sin^2(b)}}} we have


= {{{(sin(b) cos(b))/ sin^2(b)}}}


= {{{(cross(sin(b)) cos(b))/ sin^cross(2)(b)}}}


= {{{cos(b)/ sin(b)}}}


= {{{ctg(b)}}} ->={{{1/tan(b)}}}