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यदि `A+B+C=pi,` सिद्ध कीजिए कि `cos 4A+cos 4B+cos 4C=-1+4 cos 2A cos 2B cos 2C`

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यदि `A+B+C=pi,` सिद्ध कीजिए कि
`cos 4A+cos 4B+cos 4C=-1+4 cos 2A cos 2B cos 2C`
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बायाँ पक्ष `=cos4A+cos 4B+cos 4C`
`=2cos(2A+2B)cos (2A-2B)+cos 4C`
`=2cos (2pi-2C)cos(2A-2B)+(2cos^(2)2C-1)`
`=2cos 2C[cos(2A-2B)+cos{2pi-(2A+2B)}]-1`
`=2cos 2C[2cos 2A cos 2B]-1`
`=-1+4 cos 2 cos 2B cos 2C=` दायाँ पक्ष
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