Question

If tan inverse x + tan inverse y + tan inverse z = π/2
Prove xy+yz+xx=1​

Answer 1

see put x = tanA , y = tanB and z = tanC , 

then A + B + C = pi/2 and 

A+B = 90 - C 

take tan both sides we get 

tan (A+B) = tan (90-C) = cot C= 1/ tan C 

or (tan A+ tan B)/(1- tan A tan B) = 1/tan C 

cross multiply to get 

(tan A + tan B) tan C = 1 - tan A tan B 

or tan A tan C + tan B tan C = 1 - tan A tan B 

or tan A tan C + tan B tan C + tan A tan B = 1 

so xy + yz + zx = 1 

Hence proved

Answer 2

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