Inverse Trigonometric Functions - Maharashtra Board STD 12 Science Maths Questions

Q 1MCQ1 Mark

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

A
$\frac{6}{25}$
B
$\frac{24}{25}$
C
$\frac{4}{5}$
✓
$-\frac{24}{25}$

Answer: D.

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Q 2MCQ1 Mark

If $+\cos^{-1}\text{x}>\sin^{-1},$ then:

✓
$\frac{1}{\sqrt2}<\text{x}\leq1$
B
$0\leq\text{x}\leq\frac{1}{\sqrt2}$
C
$-1\leq\text{x}<\frac{1}{\sqrt2}$
D
$\text{x}>0$

Answer: A.

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Q 3MCQ1 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:

A
$0$
B
$-2$
C
$1$
✓
$2$

Answer: D.

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Q 4MCQ1 Mark

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

A
$2$
B
$3$
C
$1$
✓
none of these

Answer: D.

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Q 5MCQ1 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:

A
$0$
B
$\frac{\text{a}}{2}$
C
$\text{a}$
✓
$\frac{2\text{a}}{1-\text{a}^2}$

Answer: D.

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Q 6Solve the Following Question.(2 Marks)2 Marks

Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}>0$

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Q 7Solve the Following Question.(2 Marks)2 Marks

If $\cot\Big(\cos^{-1}\frac{3}{5}+\sin^{-1}\text{x}\Big)=0,$ find the values of x.

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Q 8Solve the Following Question.(2 Marks)2 Marks

If x > 1, then write the value of $\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ in terms of $\tan^{-1}\text{x.}$

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Q 9Solve the Following Question.(2 Marks)2 Marks

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

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Q 10Solve the Following Question.(2 Marks)2 Marks

Evaluate the following:
$\cot^{-1}\Big\{\cot\Big(-\frac{8\pi}{3}\Big)\Big\}$

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Q 11Solve the Following Question.(3 Marks)3 Marks

Solve the following equation for x:
$2\tan^{-1}(\sin\text{x})=\tan^{-1}(2\sin\text{x}),\text{x}\neq\frac{\pi}{2}.$

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Q 12Solve the Following Question.(3 Marks)3 Marks

Prove the following results
$\tan\Big(\cos^{-1}\frac{4}{5}+\tan^{-1}\frac{2}{3}\Big)=\frac{17}{6}$

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Q 13Solve the Following Question.(3 Marks)3 Marks

Prove that $\cos^{-1}\frac{4}{5}+\cos^{-1}\frac{12}{13}=\cos^{-1}\frac{33}{65}$

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Q 14Solve the Following Question.(3 Marks)3 Marks

Write the following in the simplest form:
$\tan^{-1}\Big\{\sqrt{1+\text{x}^2}-\text{x}\Big\},\text{x}\in\text{R}$

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Q 15Solve the Following Question.(3 Marks)3 Marks

Write the following in the simplest form:
$\tan^{-1}\Big\{\text{x}+\sqrt{1+\text{x}^2}\Big\},\text{x}\in\text{R}$

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Q 16Solve the Following Question.(5 Marks)5 Marks

Solve the following equation for x:
$\tan^{-1}\frac{1}{4}+2\tan^{-1}\frac{1}{5}+\tan^{-1}\frac{1}{6}+\tan^{-1}\frac{1}{\text{x}}=\frac{\pi}{4}$

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Q 17Solve the Following Question.(5 Marks)5 Marks

If $\sin^{-1}\text{x}+\sin^{-1}\text{y}=\frac{\pi}{3}$ and $\cos^{-1}\text{x}-\cos^{-1}\text{y}=\frac{\pi}{6},$ find the values of x and y.

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Q 18Solve the Following Question.(5 Marks)5 Marks

Prove that $2\tan^{-1}\bigg(\sqrt{\frac{\text{a}-\text{b}}{\text{a}+\text{b}}}\tan\frac{\theta}{2}\bigg)=\cos^{-1}\Big(\frac{\text{a}\cos\theta+b}{\text{a}+\text{b}\cos\theta}\Big)$

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Q 19Solve the Following Question.(5 Marks)5 Marks

For any a, b, x, y > 0, prove that:
$\frac{2}{3}\tan^{-1}\Big(\frac{3\text{a}\text{b}^2-\text{a}^3}{\text{b}^3-3\text{a}^2\text{b}}\Big)+\frac{2}{3}\tan^{-1}\Big(\frac{3\text{x}\text{y}^2-\text{x}^3}{\text{y}^3-3\text{x}^2\text{y}}\Big)=\tan^{-1}\frac{2\alpha\beta}{\alpha^2-\beta^2}$
where $\alpha=-\text{ax}+\text{by},\beta=\text{bx}+\text{ay}$

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Q 20Solve the Following Question.(5 Marks)5 Marks

Prove that: $\tan^{-1}\frac{2\text{a}\text{b}}{\text{a}^2-\text{b}^2}+\tan^{-1}\frac{2\text{xy}}{\text{x}^2-\text{y}^2}=\tan^{-1}\frac{2\alpha\beta}{\alpha^2-\beta^2},$where $\alpha=\text{ax}-\text{by}$ and $\beta=\text{ay}+\text{bx}.$

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Inverse Trigonometric Functions question types

Inverse Trigonometric Functions questions

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Inverse Trigonometric Functions Maths - Inverse Trigonometric Functions

Inverse Trigonometric Functions question types

Inverse Trigonometric Functions questions

Generate a Inverse Trigonometric Functions paper free