Inverse Trigonometric Functions - Gujarat Board (GSEB) STD 12 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

$\sin\Big\{2\cos^{-1}\Big(\frac{-3}{5}\Big)\Big\}$ is equal to:

$\frac{6}{25}$
$\frac{24}{25}$
$\frac{4}{5}$
$-\frac{24}{25}$

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Q 2M.C.Q (1 Marks)1 Mark

If $\tan^{-1}\frac{\text{x}+1}{\text{x}-1}+\tan^{-1}\frac{\text{x}-1}{\text{x}}=\tan^{-1}(-7),$ then the value of x is:

0
-2
1
2

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Q 3M.C.Q (1 Marks)1 Mark

The number of solutions of the equation
$\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\frac{\pi}{4}$ is:

2
3
1
none of these

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Q 4M.C.Q (1 Marks)1 Mark

If $\sin^{-1}\Big(\frac{2\text{a}}{1-\text{a}^2}\Big)+\cos^{-1}\Big(\frac{1-\text{a}^2}{1+\text{a}^2}\Big)=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ where $\text{a},\text{x}\in(0,1),$ then the value of x is:

$0$
$\frac{\text{a}}{2}$
$\text{a}$
$\frac{2\text{a}}{1-\text{a}^2}$

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Q 5M.C.Q (1 Marks)1 Mark

$2\tan^{-1}\big\{\text{cosec}\big(\tan^{-1}\text{x}\big)-\tan\big(\cot^{-1}\text{x}\big)\big\}$ is equal to:

$\cot^{-1}\text{x}$
$\cot^{-1}\text{x}$
$\tan^{-1}\text{x}$
$\text{none of these}$

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Q 61 Marks1 Mark

Evaluate the following:
$\tan^{-1}(\tan4)$

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Q 71 Marks1 Mark

Evaluate the following:
$\tan^{-1}\Big(\tan\frac{6\pi}{7}\Big)$

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Q 81 Marks1 Mark

The set of values of $\text{cosec}^{-1}\Big(\frac{\sqrt3}{2}\Big)$

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Q 91 Marks1 Mark

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{2\pi}{3}\Big)$

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Q 101 Marks1 Mark

Evaluate the following:
$\tan^{-1}(\tan1)$

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Q 112 Marks2 Marks

Write the orincipal value of $\cos^{-1}(\cos680^\circ)$

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Q 122 Marks2 Marks

Find the principal values of the following:
$\tan^{-1}\Big(2\cos\frac{2\pi}{3}\Big)$

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Q 132 Marks2 Marks

Find the principal value of the following:
$\sec^{-1}(2)$

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Q 142 Marks2 Marks

Find the principal values of the following:
$\tan^{-1}\Big(\frac{1}{\sqrt3}\Big)$

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Q 152 Marks2 Marks

Write the value of $\cos\big(\sin^{-1}\text{x}+\cos^{-1}\text{x}\big),|\text{x}|\leq1$

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Q 163 Marks3 Marks

Write the following in the simplest form:
$\sin^{-1}\Big\{\frac{\sqrt{1+\text{x}}+\sqrt{1-\text{x}}}{2}\Big\},0<\text{x}<1$

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Q 173 Marks3 Marks

Prove the following results
$\cos\Big(\sin^{-1}\frac{3}{5}+\cot^{-1}\frac{3}{2}\Big)=\frac{6}{5\sqrt{13}}$

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Q 183 Marks3 Marks

Find the principal values of the following:
$\tan^{-1}\Big(\cos\frac{\pi}{2}\Big)$

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Q 193 Marks3 Marks

If x < 0, y < 0 such that xy = 1, then write the value of tan^-1x + tan^-1y.

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Q 203 Marks3 Marks

Find the principal values of each of the following:
$\text{cosec}^{-1}\big(-\sqrt2\big)$

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Q 214 Marks4 Marks

Solve: $\cos\Big\{2\sin^{-1}\{-\text{x}\}\Big\}=0$

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Q 224 Marks4 Marks

Evaluate the following:
$\tan\Big\{2\tan^{-1}\frac{1}{5}-\frac{\pi}{4}\Big\}$

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Q 234 Marks4 Marks

Solve the following equation for x:
$\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\text{n}\pi+\frac{3\pi}{4}$

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Q 244 Marks4 Marks

Write the following in the simplest form:
$\tan^{-1}\sqrt{\frac{\text{a}-\text{x}}{\text{a}+\text{x}}},-\text{a}<\text{x}<\text{a}$

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Q 254 Marks4 Marks

If $\cos^{-1}\frac{\text{x}}{2}+\cos^{-1}\frac{\text{y}}{3}=\alpha,$ then prove that

$9\text{x}^2-12\text{xy}\cos\alpha+4\text{y}^2=36\sin^2\alpha.$

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Inverse Trigonometric Functions question types

Inverse Trigonometric Functions questions

Generate a Inverse Trigonometric Functions paper free

Inverse Trigonometric Functions Maths - Inverse Trigonometric Functions

Inverse Trigonometric Functions question types

Inverse Trigonometric Functions questions

Generate a Inverse Trigonometric Functions paper free