operatorname{cosec} 48^{circ}+operatorname{co | vedclass

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(C) माना $S = \operatorname{cosec} 48^{\circ} + \operatorname{cosec} 96^{\circ} + \operatorname{cosec} 192^{\circ} + \operatorname{cosec} 384^{\circ}$

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(C) माना $S = \operatorname{cosec} 48^{\circ} + \operatorname{cosec} 96^{\circ} + \operatorname{cosec} 192^{\circ} + \operatorname{cosec} 384^{\circ}$.सर्वसमिका $\operatorname{cosec} 	heta = \cot(	heta/2) - \cot 	heta$ का उपयोग करने पर:$S = (\cot 24^{\circ} - \cot 48^{\circ}) + (\cot 48^{\circ} - \cot 96^{\circ}) + (\cot 96^{\circ} - \cot 192^{\circ}) + (\cot 192^{\circ} - \cot 384^{\circ})$.यह एक टेलीस्कोपिंग योग है: $S = \cot 24^{\circ} - \cot 384^{\circ}$.चूँकि $\cot 384^{\circ} = \cot(360^{\circ} + 24^{\circ}) = \cot 24^{\circ}$,इसलिए $S = \cot 24^{\circ} - \cot 24^{\circ} = 0$.

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=$

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