Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

MEDIUM

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Using the identity $\sin^{- 1} (\sin x) = x, - \frac{π}{2} \leq x \leq \frac{π}{2} .$

Statement I: $\sin^{- 1} (\sin 2) = 2$

Statement II: The principal value of $\sin^{- 1} (\sin x) = x$

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Important Questions on Inverse Trigonometric Functions

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

\cot^{- 1} (21) + \cot^{- 1} (13) + \cot^{- 1} (- 8) =

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

\cos [2 \sin^{- 1} \frac{3}{4} + \cos^{- 1} \frac{3}{4}] =

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

\sin^{- 1} x + \cos^{- 1} y = 2 π / 5

, then

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

is

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

cosec [2 \cot^{- 1} (5) + \cos^{- 1} (\frac{4}{5})]

is equal to:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

x = {s i n}^{- 1} (\sin 10)

and

y = {c o s}^{- 1} (\cos 10),

then

y - x

is equal to:

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

\frac{\sin^{- 1} x}{a} = \frac{\cos^{- 1} x}{b} = \frac{\tan^{- 1} y}{c}; 0 < x < 1,

then the value of

\cos (\frac{π c}{a + b})

is:

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

\sin^{- 1} x - \cos^{- 1} x = \frac{π}{6},

then the value of

x

is

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

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

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The solution of

\tan^{- 1} 2 x + \tan^{- 1} 3 x = \frac{π}{4}

is

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

f^{'} (x) = \tan^{- 1} (\sec x + \tan x), - \frac{π}{2} < x < \frac{π}{2}

and

f (0) = 0

, then

f (1)

is equal to:

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

\cos (2 (\tan^{- 1} \frac{1}{5} + \tan^{- 1} 5)) =_______.

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The value of

\cot (\sum_{n = 1}^{19} \cot^{- 1} (1 + \sum_{p = 1}^{n} 2 p))

is:

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

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

(where,

0 < x < \frac{π}{2}

)

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

Assume that

3.13 \leq π \leq 3.15 .

The integer closest to the value of

\sin^{- 1} (\sin 1 \cos 4 + \cos 1 \sin 4),

where

1

and

4

appearing in

\sin

and

\cos

are given in radians, is:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

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

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

\sin^{- 1} x \cos^{- 1} x = p

, then the value of

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

is

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The value of

\cos^{- 1} (\cos \frac{5 π}{4})

is

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If

a + \frac{π}{2} < 2 \tan^{- 1} x + 3 \cot^{- 1} x < b

then

' a'

and

' b'

are respectively.

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The principal value of

\tan^{- 1} (\cot \frac{43 π}{4})

is

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

\sin^{- 1} \frac{3}{5} - \sin^{- 1} \frac{8}{17} =