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सिद्ध कीजिए कि `cos A+cos B+cos C+cos (A+B+C)=4cos.(A+B)/(2)cos.(B+C)/(2)cos.(C+A)/(2)` |
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Answer» बायाँ पक्ष `=cosA((A+B)/(2))cos((A-B)/(2))+2cos((A+B+2C)/(2))cos((A+B)/(2))` `=2cos((A+B)/(2))[cos((A-B)/(2))+cos((A+B+2C)/(2))]` `=2cos((A+B)/(2))cos((A-B)/(2))+2cos((A+B+2C)/(2))cos((A+B)/(2))` `=2cos((A+B)/(2))[cos((A-B)/(2))+cos((A+B+2C)/(2))]` `=2cos((A+B)/(2))[2cos.(((A-B)/(2)+(A+B+2C)/(2))/(2))cos.(((A+B+2C)/(2))-(A-B)/(2))/(2)]` `=2cos((A+B)/(2))(2cos((A+C)/(2))cos((B+C)/(2)))` `=4cos((A+B)/(2))cos((B+C)/(2))cos((C+A)/(2))=` दायाँ पक्ष |
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