Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 5

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Let $f (x) = \cos^{- 1} (\frac{1 - \tan^{2} \frac{x}{2}}{1 + \tan^{2} \frac{x}{2}})$ , then which of the following statement is/are true?

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Important Questions on Inverse Trigonometric Functions

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IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 6

If

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

and

h (x) = \cot^{- 1} (\cot x),

then which of the following is/are correct?

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Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 7

An ordered triplet solution

(x, y, z)

with

x, y, z \in (0, 1)

and satisfying

x^{2} + y^{2} + z^{2} + 2 x y z = 1

is -

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Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 8

For the equation

2 x = \tan (2 \tan^{- 1} a) + 2 \tan (\tan^{- 1} a + \tan^{- 1} a^{3})

, which of the following is/are invalid?

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 14

If the range of the function

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

is

[a, b]

then the value of

\frac{b}{a}

is

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 15

If the value of series

\sin^{- 1} \frac{1}{\sqrt{2}} + \sin^{- 1} \frac{\sqrt{2} - 1}{\sqrt{6}} + . . . + \sin^{- 1} \frac{\sqrt{n} - \sqrt{n - 1}}{\sqrt{n (n + 1)}} + . . . . . \infty

is a then the value of

\frac{π}{a}

is

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 16

Number of positive integral ordered pairs

(x, y)

which satisfy the equation

\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^{2}}} = \sin^{- 1} \frac{3}{\sqrt{10}}

is.

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 17 - Inverse Trigonometric Functions>Exercise 1>Q 17

The value

k

for which there is a triangle whose angles have measure

\tan^{- 1} (\frac{1}{2}), \tan^{- 1} (\frac{1}{2} + k)

and

\tan^{- 1} (\frac{1}{2} + 2 k)

, is