First slide

Properties of ITF

Question

If minimum value of ${(\sin^{- 1} x)}^{2} + {(\cos^{- 1} x)}^{2}$ is $\frac{π^{2}}{k}$ then the value of K is

Moderate

A

4
B

1
C

8
D

10

Solution

${(\sin^{- 1} x)}^{2} + {(\cos^{- 1} x)}^{2} =$ ${(\sin^{- 1} x)}^{2} + {(\frac{π}{2} - \sin^{- 1} x)}^{2}$
$= 2 {(\sin^{- 1} x)}^{2} - π \sin^{- 1} x + \frac{π^{2}}{4}$
Its minimum value is $\frac{4.2. \frac{π^{2}}{4} - π^{2}}{8} = \frac{π^{2}}{8}$

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