व्यंजक $\frac{1+\sin 2 \alpha}{\cos (2 \alpha-2 \pi) \tan \left(\alpha-\frac{3 \pi}{4}\right)} - \frac{1}{4} \sin 2 \alpha \left[\cot \frac{\alpha}{2}+\cot \left(\frac{3 \pi}{2}+\frac{\alpha}{2}\right)\right]$ का मान ज्ञात कीजिए।

  • A
    $0$
  • B
    $1$
  • C
    $\sin ^2 \frac{\alpha}{2}$
  • D
    $\sin ^2 \alpha$

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समीकरणों $\sin x + \sin y = \sin (x + y)$ और $|x| + |y| = 1$ को संतुष्ट करने वाले $(x, y)$ युग्मों की संख्या है

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