Question

If tan⁻¹ x + tan⁻¹ y + tan⁻¹ z = π, then prove that x + y + z = xyz.

Answer 1

Answer:

Step-by-step explanation:

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Name Harshit

Answer 2

Solution :

i ) Let tan^-1 x = A

=> x = tanA

ii ) tan^-1 y = B

=> y = tan B

iii ) tan^-1 z = C

=> z = tanC

Given A + B + C = π

=> A + B = π - C

=> tan( A + B ) = tan( π - C )

=> ( tanA + tanB )/(1-tanAtanB ) = -tanC

=> tanA+tanB = -tanC + tanAtanBtanC

=> tanA+tanB+tanC = tanAtanBtanC

=> x + y + z = xyz