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in a triangle ABC, prove that a^2cotA + b^2cotb + c^2cotc = abc\R question is from the chapter properties of triangles in a triangle ABC, prove that a^2cotA + b^2cotb + c^2cotc = abc\R question is from the chapter properties of triangles
note that sinA/a= sinB/b= sinC/c= 1/2R. so a= 2RsinA, b= 2RsinB and c= 2RsinChence, a^2cotA + b^2cotb + c^2cotc= 4R^2(sin^2A*cosA/sinA + sin^2B*cosB/sinB + sin^2C*cosC/sinC)= 2R^2(sin2A + sin2B + sin2C)but by conditional identities we know that sin2A + sin2B + sin2C= 4sinAsinBsinCso, RHS= 8R^2sinAsinBsinC= 8R^2*(a/2R)*(b/2R)*(c/2R)= abc/Rkindly approve :))
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