Q.যদি \(cot\alpha=tan(\beta+\gamma) \) হয়, তবে \(sin(\alpha+\beta+\gamma)\)= কত ? - translate in english (a) 1 (b) \(\cfrac{\sqrt3}{2}\) (c) 0 (d) \(\cfrac{1}{2}\)
Answer: A
Given \( \cot\alpha = \tan(\beta + \gamma) \) Then, \( \cot\alpha = \cot[90^\circ - (\beta + \gamma)] \) So, \( \alpha = 90^\circ - (\beta + \gamma) \) Therefore, \( \alpha + \beta + \gamma = 90^\circ \) \(\therefore\) \( \sin(\alpha + \beta + \gamma) = \sin 90^\circ = 1 \)
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