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In any A B C , prove that: a(b\ cos C-c...

In any ` A B C ,` prove that: `a(b\ cos C-ccosB)=b^2-c^2`

Text Solution

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LHS. `=a(bcosC-(c)cosB)`
`=abcosC-a(c)cosB`
`=ab.(a^(2)+b^(2)-c^(2))/(2ab)-ac.(c^(2)+a^(2)-b^(2))/(2ca)`
`=(a^(2)+b^(2)-c^(2))/(2)-(c^(2)+a^(2)-b^(2))/(2)`
`=(a^(2)+b^(2)-c^(2)-c^(2)+a^(2)-b^(2))/(2)`
`=2(b^(2)-c^(2))/(2)`
`=b^(2)-c^(2)`= RHS Hence Proved.
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