Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 64

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The set of exhaustive values of $x$ satisfying the equation $s i n (\sin^{- 1} x) = \sin^{- 1} (\sin x)$ is

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Important Questions on Inverse Trigonometric Functions

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 65

Which of the following is the range of the function

f (x) = \sqrt{x - e} (\sin^{- 1} (\ln x) + \cos^{- 1} (\ln x))

?

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 66

Consider the equation

\frac{{(\sin^{- 1} x)}^{3} + {(\cos^{- 1} x)}^{3}}{{(\tan^{- 1} x + \cot^{- 1} x)}^{3}} = 7

, then the value of

x

is :

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 67

Which of the following is the domain of the function

f (x) = 2 s i n^{- 1} \sqrt{1 - x} + s i n^{- 1} (2 \sqrt{x (1 - x)})

?

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 68

If

x

and

y

are positive integers satisfying

\tan^{- 1} (\frac{1}{x}) + \tan^{- 1} (\frac{1}{y}) = \tan^{- 1} (\frac{1}{7}),

then the number of ordered pairs of

(x, y)

is

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 69

\cot^{- 1} (\sqrt{\cos α}) - \tan^{- 1} (\sqrt{\cos α}) = x

, then

\sin x

equals

HARD

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 70

If

\sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z = \frac{3 π}{2},

then the value of

x^{100} + y^{100} + z^{100} - \frac{9}{x^{101} + y^{101} + z^{101}}

is equal to

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 71

If

x \in (\frac{11 π}{2}, \frac{15 π}{2})

, then

\tan^{- 1} (\frac{\cos x}{1 + \sin x}) =

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Mathematics Crash Course MHT-CET>Chapter 13 - Inverse Trigonometric Functions>Exercise 1>Q 72

The number of solution of the equation

\tan^{- 1} (x - 1) + \tan^{- 1} x + \tan^{- 1} (x + 1) = \tan^{- 1} 3 x

is