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NCERT Mathematics Part-I Std 12

Inverse Trigonometric Functions

Chapter 2 : Inverse Trigonometric Functions

Q. Find the principal value of

{tan}^{- 1} (- \sqrt{3}) .

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Q. Find the principal value of

{tan}^{- 1} (- 1) .

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Q. Find the principal value of

{c o s e c}^{- 1} (- \sqrt{2})

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Q. Find the value of

{cos}^{- 1} (\frac{1}{2}) + {2 sin}^{- 1} (\frac{1}{2})

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Q. Find the principal value of

{sec}^{- 1} (\frac{2}{\sqrt{3}})

.

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Q. Find the principal value of

{cot}^{- 1} (\sqrt{3}) .

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Q. Find the principal value of

{cos}^{- 1} (\frac{\sqrt{3}}{2})

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Q. Find the range of

{sin}^{- 1} x

.

$0 \leq y \leq π$
$- \frac{π}{2} \leq y \leq \frac{π}{2}$
$- \frac{π}{2} < y < \frac{π}{2}$
$0$

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Q. Find the value of

{tan}^{- 1} \sqrt{3} - {sec}^{- 1} (- 2)

is equal to

$- \frac{π}{3}$
$\frac{π}{3}$
$\frac{2 π}{3}$
$π$

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Q. Find the principal value of

{cos}^{- 1} (- \frac{1}{\sqrt{2}})

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Q. Find the principal value of

{cos}^{- 1} (- \frac{1}{2}) .

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Q. Find the value of

{tan}^{- 1} (1) + {cos}^{- 1} (- \frac{1}{2}) + {sin}^{- 1} (- \frac{1}{2}) .

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Q. Find the principal value of

{sin}^{- 1} (- \frac{1}{2})

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Q. Find the principal value of

{cosec}^{- 1} (2) .

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Q. Write the function in the simplest form:

{tan}^{- 1} \frac{1}{\sqrt{x^{2} - 1}}, | x | > 1

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Q. Write the function in the simplest form:

{tan}^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x}, x \neq 0

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Q.

Prove: $3 {sin}^{- 1} x = {sin}^{- 1} (3 x - {4 x}^{3}), x \in [- \frac{1}{2}, \frac{1}{2}]$

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Q. Prove:

{tan}^{- 1} \frac{2}{11} + {tan}^{- 1} \frac{7}{24} = {tan}^{- 1} \frac{1}{2}

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Q. Prove:

3 {cos}^{- 1} x = {cos}^{- 1} ({4 x}^{3} - 3 x), x \in [\frac{1}{2}, 1]

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Q. Prove:

2 {tan}^{- 1} \frac{1}{2} + {tan}^{- 1} \frac{1}{7} = {tan}^{- 1} \frac{31}{17}

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