Question 813090
prove identity
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
***
{{{2tan(x)sec(x)=1/(1-sin(x))-1/(1+sin(x))}}}
Start with right side:
{{{1/(1-sin(x))-1/(1+sin(x))}}}
LCD:(1+sin(x))(1-sin(x))=1-sin^2(x)
{{{((1+sin(x))-(1-sin(x)))/(1-sin(x))(1+sin(x))}}}
{{{(1+sin(x)-1+sin(x))/(1-sin(x))(1+sin(x))=(2sin(x))/(1-sin^2(x))
=(2sin(x))/(cos^2(x))=(2sin(x)/cos(x))(1/(cos(x)))=(2tan(x))(sec(x))}}}

verified: right side=left side