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Prove thatCot18+Cot30=Cosec12 |
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Answer» LHS = Cot18+Cot30 = \({cos18^o\over sin18^o}+ {\sqrt3}\) =\({cos18^o+\sqrt3sin18^o \over sin18^o}\) =\({2(sin30^ocos18^o+\cos30^osin18^o )\over sin18^o}\) =\({2sin(30^o+18^o)\over sin18^o}\) =\({2sin48^o\over sin18^o}\) =\({2sin48^osin12^o\over sin18^osin12^o}\) =\({cos36^o -cos60^o\over sin18^osin12^o}\) =\({{{\sqrt{5} +1\over 4}-{1\over2} }\over sin18^osin12^o}\) =\({{{\sqrt{5} -1\over 4}}\over sin18^osin12^o}\) = \({{sin18^o}\over sin18^osin12^o}\) = \({cosec12^o}\) =RHS proved |
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