Question

a) If x + y + z = xy + yz + zx, show that
Z-X
a?
a
X-y
a 1-2
La
= 1
Q
a?​

Answer 1

ANSWER

tan

−1

x+tan

−1

y+tan

−1

z=

2

π

Let tan

−1

x=α

⇒tanα=x

tan

−1

y=β

⇒tanβ=y

tan

−1

z=γ

⇒tanγ=z

⇒α+β+γ=

2

π

tan(α+β+γ)=

1−(tanαtanβ+tanβtanγ+tanγtanα)

tanα+tanβ+tanγ−tanαtanβtanγ

=tan

2

π

=not defined

⇒ Denominator=0

⇒tanαtanβ+tanβtanγ+tanγtanα=1

⇒xy+yz+zx=1.