Question

Verify the Identity: (1/1+sin(x))+(1/1-sin(x))=2Sec^2(x)

Answer 1

\[{1\over 1+sinx} +{1\over 1-sinx}\]multiply the left fraction num. and denom. by 1-sinx and the right fraction by 1+sinx\[{1-sinx\over (1-sin^{2}x)} + {1+sinx\over 1-sin^{2}x}\]Use the identity \[1-sin^{2}x=cos^{2}\] and expand the fractions\[{1\over cos^{2}} -{sinx\over cos^{2}x}+{1\over cos^{2}x}+{sinx\over cos^{2}x}\]which simplifies to \[2\over cos^{2}x\]or \[2sec^{2}x\]

Answer 2

I left out the fact that \[sec(x)={1\over cos(x)}\]

Answer 3

oh my god. ritacame you saved my life LOL XDDDDDDD!!! thank you!