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Using vector method in a triangle , prov...

Using vector method in a triangle , prove that,
(ii) cos A =`(b^2+c^2-a^2)/(2bc)`.

Text Solution

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According to Fig .2.59, `veca+vecc=vecb`
(ii) `b^2 =vecb*vecb=(veca+vecc)*(veca+vecc)=veca*veca+vecc*vecc+2vecc*vecc`
`=a^2+c^2+2ac cos theta`
`=a^2+c^2+2ac cos (180^@-B)`
`=a^2+c^2-2ac cos B`
Similarly , `a^2=b^2+c^2-2bc cos A `
`or, cos A =(b^2+c^2-c^2)/(2bc)`.
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