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Prove that: (b^(2)+c^(2)-a^(2))tanA=(c...

Prove that:
`(b^(2)+c^(2)-a^(2))tanA=(c^(2)+a^(2)-b^(2))tanB`

Text Solution

Verified by Experts

LHS `=(b^(2)+c^(2)-a^(2))tanA`
`=(b^(2)+c^(2)-a^(2))/(2bc).2bc.(sinA)/(cosA)`
`=cosA.2bc.a/(kcosA)=(2abc)/k`
RHS `=(c^(2)+a^(2)-b^(2))tanB`
`=(c^(2)+a^(2)-b^(2))/(2ca).2ca(sinB)/(cosB)`
`=cosB.2ca.b/(kcosB)=(2abc)/k`
`therefore LHS=RHS` Hence Proved.
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