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Questions >> CBSE XII >> Math >> Inverse Trigonometric Functions

The result $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\bigg(\Large {\frac{x-y}{1+xy}}\normalsize \bigg)$ is true when value of xy is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

If $y=2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ for all x,then _< y < ___.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of expression $\tan\bigg(\Large \frac{\sin^{-1}x+\cos^{-1}x}{2} \normalsize\bigg),when\;x=\frac{\sqrt 3}{2}$ is _______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos(\sin^{-1}x+\cos^{-1}x),|x|\leq 1$ is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos^{-1}\bigg(\cos\frac{14\pi}{3}\bigg)$ is _____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The principal value of $\tan^{-1}\sqrt 3$ is _______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The set of values of $\sec^{-1}\big(\frac{1}{2}\big)$ is ______________.

asked Dec 21, 2012 by sreemathi.v

1 answer

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

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\sin^{-1}\bigg(\sin\frac{3\pi}{5}\bigg)$ is ________________.

asked Dec 21, 2012 by sreemathi.v

1 answer

The principal value of $\cos^{-1}\bigg(-\Large {\frac{1}{2}}\normalsize \bigg)$ is_____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

If $\cos^{-1}x\;>\;\sin^{-1}x,$ then $\begin{array}{1 1}(A)\quad\frac{1}{\sqrt 2}<x\leq 1& (B)\quad 0\leq x<\frac{1}{\sqrt 2}\\(C)\quad -1\leq x<\frac{1}{\sqrt 2} & (D)\quad x>0\end{array}$

asked Dec 21, 2012 by sreemathi.v

1 answer

The number of real solutions of the equation $\sqrt{1+\cos2x}=\sqrt 2\cos^{-1}(\cos x)\;in\begin{bmatrix}\frac{\Large \pi}{2},\pi\end{bmatrix}$

asked Dec 21, 2012 by sreemathi.v

1 answer

If $\cos^{-1}\alpha+\cos^{-1}\beta+\cos^{-1}\gamma=3\pi$ ,then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ equals $(A)\;0\quad(B)\quad 1\quad(C)\quad 6\quad(D)\quad 12$

asked Dec 21, 2012 by sreemathi.v

1 answer

If $|\;x\;|\leq 1,then\;2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ is equal to:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of the expression $\tan\bigg(\frac{1}{2}\cos^{-1}{\frac{2}{\sqrt 5}}\bigg)$ is:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cot\bigg(\cos^{-1}\frac{7}{25}\bigg)$ is

asked Dec 21, 2012 by sreemathi.v

1 answer

If $\sin^{-1}\frac{2a}{1+a^2} +\cos^{-1}\frac{1-a^2}{1+a^2}=\tan^{-1}\frac{2x}{1-x^2},where\; a,x,\in\;[0,1],$ then the value of x is

asked Dec 21, 2012 by sreemathi.v

1 answer

If $\tan^{-1}x+\tan^{-1}y=\frac{4\pi}{5},then\;\cot^{-1}x+\cot^{-1}y$ equals:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of the expression $2\sec^{-1}2+\sin^{-1}\frac{1}{2}$ is:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cos^{-1}\bigg(\cos\frac{3\pi}{2}\bigg)$ is equal to:

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\sin(\tan^{-1}(.75))$ is equal to

asked Dec 20, 2012 by sreemathi.v

1 answer

If $\cos\bigg(\sin^{-1}\frac{2}{5}+\cos^{-1}x\bigg)=0$ ,then x is equal to

asked Dec 20, 2012 by sreemathi.v

1 answer

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

asked Dec 20, 2012 by sreemathi.v

1 answer

The domain of the function $\cos^{-1}(2x-1)$ is

asked Dec 20, 2012 by sreemathi.v

1 answer

The value of $\sin^{-1}\bigg(\cos\frac{33\pi}{5}\bigg)$ is

asked Dec 20, 2012 by sreemathi.v

1 answer

If $3\tan^{-1}x+\cot^{-1}x=\pi$ then $x$ equals

asked Dec 20, 2012 by sreemathi.v

1 answer

Which of the following is the principal value branch of $\text{cosec}^{-1}x$ ?

asked Dec 20, 2012 by sreemathi.v

1 answer

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

asked Dec 20, 2012 by sreemathi.v

1 answer

If $a_1,a_2,a_3,......a_n$ is an arithmetic progression with common difference d,then evaluate the following expression $\tan \bigg( \tan^{-1}\bigg(\frac{d}{1+a_1a_2}\bigg)+\tan^{-1}\bigg(\frac{d}{1+a_2a_3}\bigg)+\tan^{-1}\bigg(\frac{d}{1+a_3a_4}\bigg)+........+\tan^{-1}\bigg(\frac{d}{1+a_{n-1}a_n}\bigg) \bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

What is the value of $\tan({\frac{1}{2}}\sin^{-1}{\frac{3}{4}})$ ?

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of $4\tan^{-1}{\large \frac{1}{5}}$ $-\tan^{-1}{\large\frac{1}{239}}$

asked Dec 20, 2012 by sreemathi.v

1 answer

What does $\tan^{-1}{\frac{1}{4}}+\tan^{-1}{\frac{2}{9}}$ reduce to?

asked Dec 20, 2012 by sreemathi.v

1 answer

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

asked Dec 20, 2012 by sreemathi.v

1 answer

Prove that $\sin^{-1}{\frac{8}{17}}+\sin^{-1}{\frac{3}{5}}=\sin^{-1}{\frac{77}{85}}$

asked Dec 20, 2012 by sreemathi.v

1 answer

Solve the following equation $\cos\big(\tan^{-1}x\big)=\sin\bigg(\cot^{-1}{\frac{3}{4}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Show that $\cos\bigg(2\tan^{-1}{\frac{1}{7}}\bigg)=\sin\bigg(4\tan^{-1}{\frac{1}{3}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

If $2\tan^{-1}(\cos x)=\tan^{-1}(2cosecx)$ ,then what is the value of $x$ ?

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of the expression $\sin \bigg(2\tan^{-1}{\frac{1}{3}}\bigg)+\cos \big(\tan^{-1}2\sqrt 2\big)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the real solution of the equation <BR> $\tan^{-1}\sqrt{x(x+1)}+\sin^{-1}\sqrt{x^2+x+1}=\frac{\pi}{2}$

asked Dec 20, 2012 by sreemathi.v

1 answer

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

asked Dec 20, 2012 by sreemathi.v

1 answer

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

asked Dec 20, 2012 by sreemathi.v

1 answer

Prove the following: $2 \: tan^{-1} \frac{1}{2} + tan ^{-1} \frac{1}{7} = tan^{-1} \frac{31}{17}$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: $tan^{-1} \frac{\sqrt {1 + x^2} - 1}{x}, x \neq 0$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: $tan^{-1} \frac{1}{\sqrt{x^2 - 1}}, | x | > 1$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: $tan^{-1} \bigg( \sqrt {\frac{1-cos \: x}{1 + cos \: x}} \bigg), x < \pi$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: $tan^{-1} \bigg( \frac{cos\: x - sin\: x}{cos\: x + sin\: x} \bigg) , 0 < x < \pi$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following in the simplest form: $\tan^{-1} \large \frac{x}{\sqrt {a^2 - x^2}},$ $| x | < a$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: $tan^{-1} \bigg( \frac{3a^2x-x^3}{a^3-3ax^2} \bigg), a > 0 ; \frac{-a}{\sqrt 3} \leq x \leq \frac{a}{\sqrt 3}$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the value of $\tan^{-1} \bigg[ 2\cos \bigg(2\sin^{-1}\frac{1}{2}\bigg) \bigg]$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the value of $\cot \;( \tan^{-1}a + \cot^{-1}a)$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

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