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If A+B+C=180 , prove that cos^2A+cos^2B+...

If `A+B+C=180 ,` prove that `cos^2A+cos^2B+cos^2C=1-2cosAcosBcosCdot`

Text Solution

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`cos^(2)A+cos^(2)B+cos^(2)C`
`=(1+cos 2A)/(2)+(1+cos 2B)/(2)+(1+cos 2C)/(2)`
`=(1)/(2)(cos 2A+cos 2B+cos 2C)+(3)/(2)`
`(1)/(2)(-1-4cos A cos B cos c)+(3)/(2)`
`=1-2cos A cos B cos C`
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