1.

If A+B+C=pi, then prove the following. cos^2A+cos^2B+2cosA cdot cosB cdot cos C=sin^2 C

Answer»

SOLUTION :`cos^2A+cos^2B+cos^2C`
`=(1+cos2A)/2+(1+cos2B)/2+(1+cos2C)/2
`(3+cos2A+cos2B+cos2C)/2`
`=(3-1-4cosAcosBcosC)/2`
`=(2-4cosAcosBcosC)/2`
`1-2cosAcosBcosC`
or, `cos^2A+cos^2B+2cosAcosBcosC`
`=1-cos^2C=sin^2C`


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