Question:medium

If $ \cos\theta + \sin\theta = \sqrt{2}\cos\theta $ and $ 0<\theta<\frac{\pi}{2} $, then $ \sec(2\theta) + \tan(2\theta) = $

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The expression $ \sec(x) + \tan(x) $ simplifies to $ \tan(\frac{x}{2} + \frac{\pi}{4}) $. Alternatively, the identity $ \frac{1+\sin(2\theta)}{\cos(2\theta)} = \frac{1+\tan\theta}{1-\tan\theta} $ is a very useful shortcut for this type of problem.

Updated On: Mar 30, 2026

$ \cot\theta $
$ \tan\theta $
$ \cos\theta $
$ \sin\theta $

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The Correct Option is A

Solution and Explanation

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If \( \cos\theta + \sin\theta = \sqrt{2}\cos\theta \) and \( 0<\theta<\frac{\pi}{2} \), then \( \sec(2\theta) + \tan(2\theta) = \)

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The Correct Option is A

Solution and Explanation

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