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सिद्ध कीजिए कि `2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)+1=0`

Answer» बायाँ पक्ष `=2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)+1`
`=2[(sin^(2)theta)^(3)+(cos^(2)theta)^(3)]-3(sin^(4)theta+cos^(4)theta)+1`
`=2(sin^(2)theta+cos^(2)theta)(sin^(4)theta+cos^(4)theta-sin^(2)thetacos^(2)theta)-3(sin^(4)theta+cos^(4)theta)+1`
`=2sin^(4)theta+2cos^(4)theta-2sin^(2)theta cos^(2)theta-3sin^(4)theta-3cos^(4)theta+1`
`=1-(sin^(4)theta+cos^(4)theta+2sin^(2)thetacos^(2)theta)=1-(sin^(2)theta+cos^(2)theta)^(2)`
`=1-1=0=` दायाँ पक्ष


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