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If in a "Delta"A B C ,(cosA)/a=(cosB)/b=...

If in a `"Delta"A B C ,(cosA)/a=(cosB)/b=(cosC)/c ,` then find the measures of angles `A ,\ B ,\ Cdot`

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It is given that` cos A/a​=cos B/b​=cos C/c`
​ Sine rule tells us that, `sin A/a​=sin B/b​=sin C/c​=1/(2R)`
⇒`(cos A​)/(2Rsin A)​=(cos B)/(2Rsin B)​=(cos C​ )/(2Rsin C)`,
∴tan A=tan B=tan C
Thus, the triangle is equilateral.
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