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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\frac{\sqrt{2}-\sin \alpha-\cos \alpha}{\sin \alpha-\cos \alpha}=\)

  1. A \(\sec \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)
  2. B \(\cos \left(\frac{\pi}{8}-\frac{\alpha}{2}\right)\)
  3. C \(\tan \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)
  4. D \(\cot \left(\frac{\alpha}{2}-\frac{\pi}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\tan \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)

Step-by-step Solution

Detailed explanation

\( \frac{\sqrt{2}-(\sin \alpha+\cos \alpha)}{\sin \alpha-\cos \alpha} = \frac{\sqrt{2}-\sqrt{2}\cos(\alpha-\frac{\pi}{4})}{\sqrt{2}\sin(\alpha-\frac{\pi}{4})} \) \( = \frac{1-\cos(\alpha-\frac{\pi}{4})}{\sin(\alpha-\frac{\pi}{4})} \)…