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I attached the problem as a file:

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Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?

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$\sin^2 t+\cos^2 t=1$ for any $t$. –  Artem Nov 28 '12 at 14:25
    
Oh, they just factored out $e^{-2t}$, and then combined the trig terms together? –  Mack Nov 28 '12 at 14:36
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1 Answer

up vote 3 down vote accepted

$$ \begin{align} & (\sin(t)+\cos(t))^2+(\sin(t)-\cos(t))^2 \\ & = \sin^2(t)+\cos^2(t)+2\cos(t)\sin(t)+\sin^2(t)+\cos^2(t)-2\cos(t)\sin(t) \\ & =2(\sin^2(t)+\cos^2(t)) \\ & =2 \end{align}$$

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Could you perhaps use latex? –  Mack Nov 28 '12 at 14:34
    
Oh, I see. Thank you very much!! –  Mack Nov 28 '12 at 14:40
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