First slide

Properties of ITF

Question

If $T a n^{- 1} x + T a n^{- 1} y + T a n^{- 1} z = \frac{π}{2}$ then

Moderate

A

$x y + y z + z x = 1$
B

$x^{2} + y^{2} + z^{2} + 2 x y z = 1$
C

$x + y + z = x y z$
D

None of these

Solution

$L e t \tan^{- 1} x = A, \tan^{- 1} y = B a n d \tan^{- 1} z = C \Rightarrow \tan A = x, \tan B = y a n d \tan C = z$
Now $\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = \frac{π}{2}$ $\Rightarrow A + B + C = \frac{π}{2}$
$\Rightarrow \tan A \tan B + \tan B \tan C + \tan C \tan A = 1 \Rightarrow x y + y z + z x = 1$

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