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TS EAMCET · Maths · Trigonometric Ratios & Identities

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

  1. A \(\cot \theta\)
  2. B \(\tan \theta\)
  3. C \(\cos \theta\)
  4. D \(\sin \theta\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\cot \theta\)

Step-by-step Solution

Detailed explanation

\(\sin \theta = (\sqrt{2}-1) \cos \theta\) \(\tan \theta = \sqrt{2}-1\) \(\sec 2 \theta+\tan 2 \theta = \frac{1+\tan \theta}{1-\tan \theta}\) \(= \frac{1+(\sqrt{2}-1)}{1-(\sqrt{2}-1)}\) \(= \frac{\sqrt{2}}{2-\sqrt{2}}\) \(= \frac{\sqrt{2}(2+\sqrt{2})}{(2-\sqrt{2})(2+\sqrt{2})}\)…