Question 965160
Prove:
csc^2 x/2 = 2 sec X/ sec -1
start with right side:
{{{2secx/secx-1}}}
{{{(2/cosx)/(1/cosx-1)}}}
{{{(2/cosx)/((1-cosx)/(cosx))}}}
{{{2/(1-cosx)=1/sin^2(x/2)=csc^2(x/2)}}}
verified: right side=left side
notes:
{{{sin(x/2)=sqrt((1-cosx)/2)}}}
{{{sin^2(x/2)=(1-cosx)/2}}}
{{{csc^2(x/2)=1/sin^2(x/2)=2/(1-cosx)}}}