Question

if A+B+C=180 prove that tanA. tanB+tanB.tanC+tanC.tanA=1​

Answer 1

Answer:

To prove: tanA+tanB+tanC =  tanA.tanB.tanC

given that ,

A+B+C=180°

A+B = 180° - C

=> tan(A+B) = tan(180° - C)

=> tan(A+B) = −tanC

=>  $\frac{tanA+tanB}{1-tanA.tanB}$ = −tanC

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

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

=> tanA+tanB =  tanA.tanB.tanC-tanC

=> tanA+tanB+tanC =  tanA.tanB.tanC

Hence proved