Question 5053
in any proof, pick one of the 2 sides and manipulate it until you get the other side. Always start with the more complicated side too!


Looking at your proof: {{{1/(1+cosx) = 1/(sin^2(x)) - 1/(sinxtanx)}}}, the RighHand side looks more complicated, so i shall pick this..basically i have more things to work with...


{{{1/(sin^2(x)) - 1/(sinxtanx)}}}. I shall use the facts that tanx = sinx/cosx and also {{{sin^2(x) + cos^2(x) = 1}}}.


{{{1/(sin^2(x)) - 1/(sinx*sinx/cosx)}}}
{{{1/(sin^2(x)) - cosx/(sin^2(x))}}}
{{{(1 - cosx)/(sin^2(x))}}}
{{{(1 - cosx)/(1 - cos^2(x))}}}. Now factorise the denominator:


{{{(1 - cosx)/((1 - cosx)(1 + cosx))}}}

{{{1/(1 + cosx)}}} QED


jon.