Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 52

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The range of the function $f (x) = \cos^{- 1} \sqrt{\log_{[x]} \frac{|x|}{x}}$ , where $[\cdot]$ represents greatest integer function, is set $\{a\}$ then the fundamental period of $\sin (a x)$ is equal to

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Important Questions on Inverse Trigonometric Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 53

If

{cosec}^{- 1} (2^{x}) + \sec^{- 1} (x^{2}) = \frac{π}{2}

then number of solutions of this equation is

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 54

If

{(\sin^{- 1} x)}^{5} + {(\sin^{- 1} y)}^{5} + {(\sin^{- 1} z)}^{5} = \frac{3 π^{5}}{32}

then the value of

5 x^{2} + 17 y^{2} + 19 z^{2} + 8 x y + 5 y z + 7 z x

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 55

Number of solutions of

4 \cos^{- 1} (\cos |x|) = |x|

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 56

The value of

\cot^{2} (\cot^{- 1} 3 + \cot^{- 1} 7 + \cot^{- 1} 13 + \cot^{- 1} 21)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 57

The value of

\sin^{- 1} (\sin 9) + \tan^{- 1} (\tan 9)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 58

If

α = 3 \cos^{- 1} (\frac{5}{\sqrt{28}}) + 3 \tan^{- 1} (\frac{\sqrt{3}}{2})

and

β = 4 \sin^{- 1} (\frac{7 \sqrt{2}}{10}) - 4 \tan^{- 1} (\frac{3}{4})

then value of

5 \cos α + 10 \sec β

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 59

The range of

f (x) = \cot^{- 1} (\frac{x^{2}}{1 + x^{2}})

is

(a, b)

then

\frac{3 π}{a + b}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 60

The number of positive integers in the domain of

f (x) = \cos^{- 1} ([e^{x}] - 1) + \sin^{- 1} ([e^{x}])

, where

[\cdot]

represents greatest integer function, is equal to