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How to prove that \[ \frac12\frac1{1+\sin^2 x} + \frac12\frac1{1+\cos^2 x} + \frac12\frac1{1+\sec^2 x}+ \frac12\frac1{1+\csc^2 x} = 1? \] Some genius please help me I have been stuck at this for one whole day.

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    Please be clearer about the equation. Some would read 1/2(1+sin^2 x) as $\frac 1{2(1+\sin^2 x)}$ or at least worry that you meant that. Either (1+sin^2 x)/2, (1/2)(1+sin^2 x), or (best) $\LaTeX$. Trying to solve the problem, I see I had it wrong, so please 1/(2(1+sin^2 x)), or $\LaTeX$2012-07-24
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    I would start by getting rid of $\sec$ and $\csc$, replacing them with $\frac 1\cos$ and $\frac 1\sin$. Then you must have identities for $1+\sin^2 x$ and $1 + \cos^2 x$. Where does that take you?2012-07-24

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