Given that \(\tan\theta = 2\) and \(\theta\) is in the first quadrant, what is the value of \(\sec\theta\)?
\(\sqrt{5}\)
Using the trigonometric identity \(\sec^2\theta = 1 + \tan^2\theta\).
Substituting \(\tan\theta = 2\): \(\sec^2\theta = 1 + 2^2 = 1 + 4 = 5\).
So \(\sec\theta = \sqrt{5}\).
Since \(\theta\) is in the first quadrant, all trigonometric ratios are positive, so the positive root is taken.
Hence, the value of \(\sec\theta\) is \(\sqrt{5}\).
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