Grade 11Magical Mathematics[Interesting Approach]
how to proof:-acotA+bcotB+ccotC=2(R+r)
how to proof:-
acotA+bcotB+ccotC=2(R+r)
1 Answer
Sunil Raikwar
Hello students, please check the solution given below:
acotA + bcotB + ccotC
= 2RsinAcotA + 2RsinBcotB + 2RsinCcotC
= 2RcosA + 2RcosB +2RcosC
= 2R(cosA+cosB+cosC)
= 2R(1+4sin(A/2)sin(B/2)sin(C/2))
= 2R(1+r/R)
= 2(R+r)
acotA + bcotB + ccotC
= 2RsinAcotA + 2RsinBcotB + 2RsinCcotC
= 2RcosA + 2RcosB +2RcosC
= 2R(cosA+cosB+cosC)
= 2R(1+4sin(A/2)sin(B/2)sin(C/2))
= 2R(1+r/R)
= 2(R+r)
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