Question

If A,B,C are angles of a triangle and none of them is equal to pi/2. then prove that
tan A + tanB + tanC = tan A, tanB. tanC.​

Answer 1

Step-by-step explanation:

tan(180-ø)= -tanø

A+B+C=180

A+B=180-C

tan(A+B)=tan(180-C)

tanA+tanB/1-tanA.tanB= (-tanC)

tanA+tanB=(1-tanA.tanB)(-tanC)

tanA+tanB= 1×(-tanC) +tanA.tanB.tanC

tanA+tanB=tanA.tanB.tanC-tanC

tanA+tanB+tanC= tanA.tanB.tanC

hence proved

Note: tan(180-ø)= (-tanø)

Answer 2

Step-by-step explanation:

tan(180-ø)=-tanø

A+B+C=180

A+B=180-C

tan(A+B)=tan180-c

tanA+tanB/-tanA . tanB =(-tanC)

tanA+tanB =(1-tanA . tanB).(-tanC)

tanA+tanB=1.(-tanC)+tanA.tanB.tanC

tanA+tanB+tanC=tanA.tanB.tanC

proved

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