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Recent questions tagged ch2

Considering the principal solutions, find the number of solutions of $ \tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$

asked Jan 23, 2013 by meena.p

1 answer

Simplify $\tan^{-1}\big(\large \frac{\cos x}{1+\sin x}\big)$

asked Jan 23, 2013 by meena.p

1 answer

Solve for $x$: $\sin\bigg[\sin^{-1}\frac{1}{3}+\cos^{-1}x\bigg]=1$

asked Jan 23, 2013 by meena.p

1 answer

Find the value of $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3.$

asked Jan 23, 2013 by meena.p

1 answer

Find the value of $\cos\bigg\{\cos^{-1}\bigg(\frac{-\sqrt {3}}{2}\bigg)+\frac{\pi}{6}\bigg\}$

asked Jan 23, 2013 by meena.p

1 answer

Solve for x : \[ tan^{-1} \bigg( \frac{2x}{1-x^2} \bigg) +cot^{-1} \bigg( \frac{1-x^2}{2x} \bigg) = \frac{\pi}{3}, x > 0\]

asked Jan 23, 2013 by thanvigandhi_1

1 answer

If $ tan^{-1} \bigg(\large \frac{x-1}{x-2} \bigg) $$+ \tan^{-1} \bigg(\large \frac{x+1}{x+2} \bigg) =\large \frac{\pi}{4}, $ find the value of x.

asked Jan 22, 2013 by thanvigandhi_1

1 answer

Prove that : \[ sin^{-1}\frac{3}{5}+sin^{-1}\frac{8}{17}=cos^{-1}\frac{36}{85} \]

asked Jan 21, 2013 by thanvigandhi_1

1 answer

Solve \( 2tan^{-1}(cos \: x)=tan^{-1}(2 cosec \: x)\)

asked Jan 17, 2013 by thanvigandhi_1

1 answer

If \( cos^{-1}x+cos^{-1}y+cos^{-1}z=\pi\) prove that \( x^2+y^2+z^2+2xyz=1\)

asked Jan 17, 2013 by thanvigandhi_1

1 answer

Prove that : $ \cos^{-1}\large \frac{4}{5}+\tan^{-1}\large\frac{3}{5}$$=\tan^{-1}\large\frac{27}{11} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Prove that : \( tan^{-1}\bigg(\frac{1}{3} \bigg)+tan^{-1}\bigg(\frac{1}{5}\bigg)+tan^{-1}\bigg(\frac{1}{7}\bigg)+tan^{-1}\bigg(\frac{1}{8}\bigg)=\large\frac{\pi}{4} \)

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Write the following functions in the simplest form : \[ (i) tan^{-1} \bigg( \frac{\sqrt{1+x^2} - 1}{x} \bigg), x \neq 0 \] \[(ii) tan^{-1} \frac{1}{\sqrt{x^2-1}} ,| x | > 1 \]

asked Dec 31, 2012 by thanvigandhi_1

1 answer

Solve for \( x : \sin^{-1} (1-x)-2 \sin^{-1}\: x = \large\frac{\pi}{2} \)

asked Dec 29, 2012 by thanvigandhi_1

1 answer

Prove that \( tan^{-1} \bigg(\frac{\large 1}{\large 4} \bigg) + tan^{-1} \bigg( \frac{\large 2}{\large 9} \bigg ) = \frac{\large 1}{\large 2} cos^{-1} \bigg( \frac{3}{5} \bigg). \)

asked Dec 26, 2012 by thanvigandhi_1

1 answer

Simplify\( 2\tan^{-1} \bigg(\large \frac{1}{5} \bigg) + \sec^{-1} \bigg( \large\frac{5\sqrt 2}{7} \bigg) + 2\: tan^{-1} \bigg( \frac{1}{8} \bigg) \)

asked Dec 25, 2012 by thanvigandhi_1

1 answer

True or False: The principal value of $\sin^{-1}\begin{bmatrix}\cos\bigg(\sin^{-1}\frac{1}{2}\bigg)\end{bmatrix}\;is\;\Large {\frac{\pi}{3}}$

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False:The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The least numerical value, either positive or negative of angle $\theta$ is called principal value of the inverse trigonometric function.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The domain of trigonometric functions can be restricted to any one of their branch(not necessarily principal value) in order to obtain their inverse function.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The value of the expression $(\cos^{-1}x)^2$ is equal to $\sec^2x.$

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: All trigonometric functions have inverse over their respective domains.

asked Dec 21, 2012 by sreemathi.v

1 answer

The value of $\cot^{-1}(-x)$ for all $x\;\in\;R$ in terms of $\cot^{-1}x$ is ____________.

asked Dec 21, 2012 by sreemathi.v

1 answer

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

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