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Inverse Trigonometric Functions

Multiple Choice Questions

41.

The doamin of $\sin^{- 1} [\log_{2} (\frac{x}{12})]$ is

[2, 12]
[- 1, 1]
$[\frac{1}{3}, 24]$
[6, 24]

42.

If $\tan^{- 1} (x + 2) + \tan^{- 1} (x - 2) - \tan^{- 1} (\frac{1}{2}) = 0$ , then one of the values of x is equal to

- 1
5
$\frac{1}{2}$
1

43.

The value of $\sin^{- 1} (\frac{4}{5}) + 2 \tan^{- 1} (\frac{1}{3})$ is equal to

$\frac{π}{3}$
$\frac{π}{4}$
$\frac{π}{2}$
$\frac{π}{6}$

44.

The value of $\sin^{- 1} (\cos (4095 °))$ is equal to

$- \frac{π}{3}$
$\frac{π}{6}$
$- \frac{π}{4}$
$\frac{π}{4}$

45.
If $2 \sin^{- 1} (x) - \cos^{- 1} (x) = \frac{π}{2}$ , then x is equal to

$\frac{1}{\sqrt{2}}$

$- \frac{1}{\sqrt{2}}$

$\frac{- \sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

$2 \sin^{- 1} (x) - \cos^{- 1} (x) = \frac{π}{2} \Rightarrow 2 \sin^{- 1} (x) + 2 \cos^{- 1} (x) - 2 \cos^{- 1} (x) - \cos^{- 1} (x) = \frac{π}{2} \Rightarrow 2 (\sin^{- 1} (x) + \cos^{- 1} (x)) - 3 \cos^{- 1} (x) = \frac{π}{2} \Rightarrow 2 . \frac{π}{2} - 3 \cos^{- 1} (x) = \frac{π}{2} [∵ \sin^{- 1} (x) + \cos^{- 1} (x) = \frac{π}{2}] \Rightarrow π - \frac{π}{2} = 3 \cos^{- 1} (x) \Rightarrow \frac{π}{2} = 3 \cos^{- 1} (x) \Rightarrow \cos^{- 1} (x) = \frac{π}{6} \Rightarrow x = \cos (\frac{π}{6}) \Rightarrow x = \frac{\sqrt{3}}{2}$