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$\dfrac{(1-\sec^4\theta)(1-\sin^4\theta)}{\sin^2\theta-2}$

When simplifying the expressions above, how can I eliminate the denominator?

I have tried expanding the nominators by $a^4-1=(a^2-1)(a^2+1)$ but I still cannot remove that obstacle. Can anyone give me some hints to deal with the denominator?

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Hint: I observe that ${\sin^2\theta-2} = {-(\cos^2\theta + 1)}$, which will (with a factor modification) cancel with one of those factors you might see from the numerator.

Does that help?

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  • $\begingroup$ Thank you very much!!! I have never thought of changing the denominator like that :) $\endgroup$ – redcap Apr 23 '13 at 15:12

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