Question 914721
Verify the following trig identities
1) sin^2x/cosx=secx-cosx
{{{sin^2(x)/cos(x)
=(1-cos^2(x))/cos(x)
=1/cos(x)-cos^2(x)/cos(x)
=sec(x)-cos(x)}}}
..
2) 1+sinx/1-sinx - 1-sinx/1+sinx = 4tanx secx
{{{(1+sinx)/(1-sinx)-(1-sinx)/(1+sinx)}}}
{{{((1+sinx)^2-(1-sinx)^2)/(1+sinx)(1-sinx))}}}
{{{((1+2sinx+sin^2(x))-(1-2sinx+sin^2(x)))/(1-sin^2(x))}}}
{{{(1+2sinx+sin^2(x)-1+2sinx-sin^2(x))/(1-sin^2(x))}}}
{{{(4sinx/cos^2(x))=(4sinx/cosx)(1/cosx)=4tanxsecx}}}
..
3) sin^3x+cos^3x = (cosx+sinx)(1-cosx sinx)
{{{sin^3(x)+cos^3(x)=(sinx+cosx)(sin^2(x)-sinxcosx+cos^2(x))=(sinx+cosx)(1-sinxcosx)}}}
note: use sum of cubes formula