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For the Principal Value, Evaluate the Following: ${Tan}^{- 1} \sqrt{3} - \sec^{- 1} (- 2)$ - Mathematics

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प्रश्न

For the principal value, evaluate the following:

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

उत्तर

$\tan^{- 1} \sqrt{3} - \sec^{- 1} (- 2) = \tan^{- 1} (\tan \frac{π}{3}) - \sec^{- 1} (\sec \frac{2 π}{3})$

$= \frac{π}{3} - \frac{2 π}{3}$

$= - \frac{π}{3}$

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Inverse Trigonometric Functions - Inverse Trigonometric Functions - Principal Value Branch

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 2.1 Q 1.4 Q 2.2

पाठ 4: Inverse Trigonometric Functions - Exercise 4.04 [पृष्ठ १८]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 4 Inverse Trigonometric Functions
Exercise 4.04 | Q 2.1 | पृष्ठ १८

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संबंधित प्रश्‍न

Prove that $\sin^{- 1} (\frac{3}{5}) + \cos^{- 1} (\frac{12}{13}) = \sin^{- 1} (\frac{56}{65})$

Find the principal value of the following:

$\sin^{- 1} (\cos \frac{3 π}{4})$

For the principal value, evaluate of the following:

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

For the principal value, evaluate of the following:

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

Find the principal value of the following:

$\tan^{- 1} (\cos \frac{π}{2})$

Find the principal value of the following:

$\tan^{- 1} (2 \cos \frac{2 π}{3})$

Find the principal value of the following:

$\sec^{- 1} (2)$

Find the principal value of the following:

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

For the principal value, evaluate the following:

$\sin^{- 1} (- \frac{\sqrt{3}}{2}) + {cosec}^{- 1} (- \frac{2}{\sqrt{3}})$

Find the principal value of the following:

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

Find the principal value of the following:

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

Find the principal value of the following:

$\cot^{- 1} (\tan \frac{3 π}{4})$

Show that ${sin}^{- 1} (\frac{5}{13}) + {cos}^{- 1} (\frac{3}{5}) = {tan}^{- 1} (\frac{63}{16})$

Show that ${sin}^{- 1} (\frac{5}{13}) + {cos}^{- 1} (\frac{3}{5}) = {tan}^{- 1} (\frac{63}{16})$

Find the value of $\tan^{- 1} (\tan \frac{9 π}{8})$ .

Which of the following corresponds to the principal value branch of tan^–1?

The value of cot (sin^–1x) is ______.

The greatest and least values of (sin–¹x)² + (cos^–1x)² are respectively ______.

If sin^–1x + sin^–1y = $\frac{π}{2}$ , then value of cos^–1x + cos^–1y is ______.

The value of $\tan (\cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4})$ is ______.

The value of tan² (sec^–12) + cot² (cosec^–13) is ______.

Find the value of $\tan^{- 1} (\tan \frac{5 π}{6}) + \cos^{- 1} (\cos \frac{13 π}{6})$

Find the value of $\tan^{- 1} (\tan \frac{2 π}{3})$

Which of the following is the principal value branch of cosec^–1x?

The value of $\sin^{- 1} [\cos (\frac{33 π}{5})]$ is ______.

The domain of the function defined by f(x) = $\sin^{- 1} \sqrt{x - 1}$ is ______.

The value of $\cos^{- 1} (\cos \frac{3 π}{2})$ is equal to ______.

If $\cos (\tan^{- 1} x + \cot^{- 1} \sqrt{3})$ = 0, then value of x is ______.

The value of cos (sin^–1x + cos^–1x), |x| ≤ 1 is ______.

The value of the expression (cos^–1x)² is equal to sec²x.

The minimum value of n for which $\tan^{- 1} \frac{n}{π} > \frac{π}{4}$ , n ∈ N, is valid is 5.

The principal value of $\sin^{- 1} [\cos (\sin^{- 1} \frac{1}{2})]$ is $\frac{π}{3}$ .

The period of the function f(x) = cos4x + tan3x is ____________.

If sin $({sin}^{- 1} \frac{1}{5} + {cos}^{- 1} x) = 1,$ then the value of x is ____________.

Which of the following is the principal value branch of ${cos}^{- 1} x$

Assertion (A): Maximum value of (cos^–1 x)² is π².

Reason (R): Range of the principal value branch of cos^–1 x is $[\frac{- π}{2}, \frac{π}{2}]$ .

Evaluate $\sin^{- 1} (\sin \frac{3 π}{4}) + \cos^{- 1} (\cos π) + \tan^{- 1} (1)$ .

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