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Inverse Trigonometric Functions

Multiple Choice Questions

141.

The value of $\sin^{- 1} (\frac{2 \sqrt{2}}{3}) + \sin^{- 1} (\frac{1}{3})$ is

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

142.

Solve for $x \tan^{- 1} (\frac{1 - x}{1 + x}) = \frac{1}{2} \tan^{- 1} (x) . x > 0$

- 1
$\sqrt{3}$
$\frac{1}{\sqrt{3}}$
1

143.

If $\frac{{(x + 1)}^{2}}{x^{3} + x} = \frac{A}{x} + \frac{Bx + C}{x^{2} + 1}$ , then $\csc^{- 1} (\frac{1}{A}) + \cot^{- 1} (\frac{1}{B}) + \sec^{- 1} (C)$ is equal to

$\frac{π}{6}$
$\frac{5 π}{6}$
$\frac{π}{2}$
0

144.

If $α \leq 2 \sin^{- 1} (x) + \cos^{- 1} (x) \leq β$ , then

$α = 0, β = π$
$α = \frac{- π}{2}, β = \frac{π}{2}$
$α = 0, β = 2 π$
$α = \frac{- π}{2}, β = \frac{3 π}{2}$

145.

The value of $\sin^{- 1} (\cos (\frac{53 π}{5}))$ is

$\frac{3 π}{5}$
$\frac{- 3 π}{5}$
$\frac{π}{10}$
$\frac{- π}{10}$

146.
If $3 \tan^{- 1} (x) + \cot^{- 1} (x) = π$ , then x is equal to

0

1

- 1

1/2

$We have, 3 \tan^{- 1} (x) + \cot^{- 1} (x) = π \Rightarrow 2 \tan^{- 1} (x) + \tan^{- 1} (x) + \cot^{- 1} (x) = π \Rightarrow 2 \tan^{- 1} (x) = π - \frac{π}{2} [∵ \tan^{- 1} (x) + \cot^{- 1} (x) = \frac{π}{2}] \Rightarrow 2 \tan^{- 1} (x) = \frac{π}{2} \Rightarrow \tan^{- 1} (x) = \frac{π}{4} \Rightarrow x = \tan (\frac{π}{4}) = 1$