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