Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 12

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If $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}$ all are independent then the maximum and minimum values of $[\sin^{- 1} x_{1}] + [\cos^{- 1} x_{2}] + [\tan^{- 1} x_{3}] + [\cot^{- 1} x_{4}] + [\sec^{- 1} x_{5}] + [{cosec}^{- 1} x_{6}]$ , where $[]$ represents greatest integer function, respectively are

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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 13

If

x + \frac{1}{x} = 2

and

[\sin^{- 1} y] = - 2

, where

[]

represents the greatest integer function, then the minimum value of

\sin^{- 1} x + \sin^{- 1} y

is

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 14

Let

[]

represents the greatest integer function and

[\cos^{- 1} \sin^{- 1} \tan^{- 1} x] = 1

then '

x

' lies in the interval

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 15

Let

f (x) = \sin^{- 1} (\frac{1}{|x^{2} - 1|}) + \cos^{- 1} (\frac{1 - 2 |x|}{3})

, then

D_{t}

is...

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 16

If

x = cosec (\tan^{- 1} (\cos (\cot^{- 1} (\sec (\sin^{- 1} a)))))

and

y = \sec (\cot^{- 1} (\sin (\tan^{- 1} (cosec (\cos^{- 1} a)))))

then

x^{2} + y^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 17

The total number of ordered pairs of

(x, y)

satisfying the equation

13 + 12 [\tan^{- 1} x] = 24 [\ln x] + 8 [e^{x}] + 6 [\cos^{- 1} y]

is/are

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 19

Let

α

be the only real root of the equation

x^{2011} + x^{2010} + x^{2009} + \dots \dots + x^{3} + x^{2} + x + a_{0} = 0

, where

a_{0}

is a positive number less than

1

then

\tan^{- 1} (α) + \tan^{- 1} (\frac{. 1}{α})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 1

Let

f (x) = \sin^{- 1} x

and

g (x) = \cos^{- 1} x

, then which of the following statements are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 2

If

\cos^{- 1} (\frac{1 - n^{2}}{1 + π^{2}}) > \frac{π}{2}

and

n \in N

, then possible values of

n

, are