Question

If tan inverse 1/x plus cot inverse 1/y plus cot inverse 1/z equal to pi/2 provethat xy+yz+zx=1

Answer 1

Answer:

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Step-by-step explanation:

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.