Question 1159694

{{{tan^2 (theta/2) = (sec( theta )- 1) / (sec (theta) + 1)}}}


manipulate left side:


{{{tan^2 (theta/2) }}}


={{{(1 - cos(theta))/(cos(theta) + 1)}}}.....since {{{cos(theta)= 1/sec(theta)}}}


={{{(1 - 1/sec(theta))/(1/sec(theta) + 1)}}}


={{{((sec(theta) - 1)/sec(theta))/((1 + sec(theta))/sec(theta))}}}


={{{((sec(theta) - 1)/cross(sec(theta)))/((1 + sec(theta))/cross(sec(theta)))}}}


={{{(sec(theta) - 1)/(1 + sec(theta))}}}-> proven