First slide

Properties of ITF

Question

The value of 'a' for which
$a x^{2} + \sin^{- 1} (x^{2} - 2 x + 2) + \cos^{- 1} (x^{2} - 2 x + 2) = 0$ has a real
solution, is

Moderate

A

$\frac{π}{2}$
B

$- \frac{π}{2}$
C

$\frac{2}{π}$
D

$- \frac{2}{π}$

Solution

We have,
$x^{2} - 2 x + 2 = (x - 1)^{2} + 1 \geq 1$ .
So, the given equation is meaningful for $x = 1 .$
Putting $x = 1,$ we have
$a + \sin^{- 1} (1) + \cos^{- 1} (1) = 0 \Rightarrow a = - \frac{π}{2}$

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