Question

1/(1 - sinx) + 1/(1 + sinx) = 2sec^2x
Prove the following identity, show all work.

Answer 1

take LHS, and take LCM

Answer 2

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Answer 3

uhh, i don't even know what the first person is saying. and um, thanks for the welcome.

I've done
\[sinx + 1 + sinx - 1\div(1-sinx)(1+sinx) = 2\div \cos^2x\]
\[2sinx \div \sin^2x = 2 \div \cos^2x\]
\[2sinx \div \cos^2x = 2 \div \cos^2x\]

I dunno what I'm supposed to do for that last part? Did I mess up somewhere?

Answer 4

\[LHS\]
\[\frac{1}{1-sinx}+\frac{1}{1+sinx}\]
taking LCM
\[\frac{1+sinx+1-sinx}{(1-sinx)(1+sinx)}\]
\[\frac{2}{\cos^{2}x}\]
\[{2\sec^{2}x}\]
\[=RHS\]