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For the expression $\sqrt{x^2-1}$, which substitution is most appropriate?
A$x=\sin\theta$
B$x=\tan\theta$
C$x=\sec\theta$
D$x=\cos\theta$
Answer & Solution
Correct answer: C. $x=\sec\theta$
If $x=\sec\theta$, then $x^2-1=\sec^2\theta-1=\tan^2\theta$, so the square root simplifies well. This is the standard substitution for $\sqrt{x^2-1}$.
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