AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\frac{\sqrt{2}-\sin \alpha-\cos \alpha}{\sin \alpha-\cos \alpha}=\)
- A \(\sec \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)
- B \(\cos \left(\frac{\pi}{8}-\frac{\alpha}{2}\right)\)
- C \(\tan \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)
- D \(\cot \left(\frac{\alpha}{2}-\frac{\pi}{2}\right)\)
Answer & Solution
Correct Answer
(C) \(\tan \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)\)
Step-by-step Solution
Detailed explanation
\( \frac{\sqrt{2}-(\sin \alpha+\cos \alpha)}{\sin \alpha-\cos \alpha} = \frac{\sqrt{2}-\sqrt{2}\cos(\alpha-\frac{\pi}{4})}{\sqrt{2}\sin(\alpha-\frac{\pi}{4})} \) \( = \frac{1-\cos(\alpha-\frac{\pi}{4})}{\sin(\alpha-\frac{\pi}{4})} \)…
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