Recent questions in Inverse Trigonometric Functions

What is the value of $cos^{-1}(-x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}(-x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $tan^{-1} \frac{1}{x}$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cos^{-1}\frac{1}{x}$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}\frac{1}{x}$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $cos^{-1}$$cos(x)$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}sinx$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

$sin^{-1}x = (sin x)^{-1}$. True or False?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\; cot^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\; sec^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\; cosec^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\tan^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\sin^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\cos^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Find the simplified form of $cos^{-1}(\frac{3}{5}cos x+\frac{4}{5}sin x),$where $x\in (\frac{-3}{4},\frac{3}{4})$

asked Feb 19, 2013 by sreemathi.v

1 answer

Prove that $tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac{1}{2}cos^{-1}x^2$

asked Feb 19, 2013 by sreemathi.v

1 answer

Show that $2tan^{-1}(-3)=\frac{-\pi}{2}+tan^{-1}\bigg(\frac{-4}{3}\bigg)$

asked Feb 19, 2013 by sreemathi.v

1 answer

Prove that \[cot(\frac{\pi}{4}-2cot^{-1}3)=7\]

asked Feb 19, 2013 by sreemathi.v

1 answer

Evaluate $cos\bigg(cos^{-1}\bigg(\frac{-\sqrt{3}}{2}\bigg)+\frac{\pi}{6}\bigg)$

asked Feb 19, 2013 by sreemathi.v

1 answer

Evaluate : \[ \frac{e^x}{\sqrt{5-4e^x-e^{2x}}}dx\]

asked Feb 15, 2013 by thanvigandhi_1

0 answers

Using the method of integration, find the area of the region bounded by the lines$ 2x+y=4, 3x-2y=6 \:and \: x-3y+5=0$

asked Feb 15, 2013 by thanvigandhi_1

0 answers

If $ \cos^{-1}\Large\frac{x}{2}+\normalsize\cos^{-1}\large\frac{y}{3}=\theta ,\;\normalsize prove\;that\;9x^2-12xy\cos\theta +4y^2=36\sin^2\theta $

asked Jan 24, 2013 by meena.p

1 answer

Solve: $\sin\lfloor2\cos^{-1}\{\cot(2\tan^{-1}x)\}\rfloor=0$

asked Jan 24, 2013 by meena.p

1 answer

Solve for x:$\tan^{-1}(x+1)+\tan^{-1}x+\tan^{-1}(x-1)=\tan^{-1}3.$

asked Jan 24, 2013 by meena.p

1 answer

Prove that $ \tan^{-1}\large\frac{yz}{xr}+ \tan^{-1}\frac{zx}{yr}+ \tan^{-1}\frac{xy}{zr}=\frac{\pi}{2}\;where\;x^2+y^2+z^2=r^2$

asked Jan 24, 2013 by meena.p

1 answer

Prove: $\cos^{-1}x-\cos^{-1}y=\cos^{-1}\bigg[xy+\sqrt{1-x^2}.\sqrt{1-y^2}\bigg]$

asked Jan 24, 2013 by meena.p

1 answer

Solve for x $ \sin^{-1}\frac{2\alpha}{1+\alpha^2}+ \sin^{-1}\frac{2\beta}{1+\beta^2}=2\tan^{-1}x.$

asked Jan 24, 2013 by meena.p

1 answer

Prove that :$\cot^{-1}\bigg[\frac{ab+1}{a-b}\bigg]+\cot^{-1}\bigg[\frac{bc+1}{b-c}\bigg]+\cot^{-1}\bigg[\frac{ca+1}{c-a}\bigg]=0$

asked Jan 24, 2013 by meena.p

1 answer

If $ x= cosec \lfloor\tan^{-1}\{\cos(\cot^{-1}(\sec(\sin^{-1}a)))\}\rfloor\; $ and $ y=\sec\lfloor\cot^{-1}\{\sin(\tan^{-1}(cosec(\cos^{-1}a)))\}\rfloor\;$ where $\;a\;\in [0,1]$ Find the relationship between $x$ and $y$ in terms of $a$

asked Jan 24, 2013 by meena.p

1 answer

In any Triangle ABC, if $ A=\tan^{-1}2\;and\;B=\tan^{-1}3,$prove that $C=\frac{\pi}{4}$

asked Jan 24, 2013 by meena.p

1 answer

Prove that $\sin2[\cot^{-1}\{\cos(\tan^{-1}x)\}]=2\frac{\sqrt{x^2+1}}{x^2+2}$

asked Jan 24, 2013 by meena.p

1 answer

If $ \sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$ prove that $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$

asked Jan 23, 2013 by meena.p

1 answer

If $ \cos^{-1}\frac{x}{a}+\cos^{-1}\frac{y}{b}=\alpha,$prove that $\frac{x^2}{a^2}-\frac{2xy}{ab}\cos \alpha+\frac{y^2}{b^2}=\sin^2\alpha.$

asked Jan 23, 2013 by meena.p

1 answer

If $x,y,z \in [-1,1]\;$ such that $\;\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\frac{3\pi}{2},$ find the value of $x^{2006}+y^{2007}+z^{2008}-\Large \frac{9}{x^{2006}+y^{2007}+z^{2008}}$

asked Jan 23, 2013 by meena.p

1 answer

Prove that $\cos\bigg\{2\cot^{-1}\sqrt{\large\frac{1-x}{1+x}}\bigg\}+x=0$

asked Jan 23, 2013 by meena.p

1 answer

If $x>0$ and $\sin^{-1}\bigg(\large{\frac{5}{x}}\bigg)+\sin^{-1}\bigg(\frac{12}{x}\bigg)=\large\frac{\pi}{2},$ than find the value of $x$.

asked Jan 23, 2013 by meena.p

1 answer

If $\cos^{-1}x=\tan^{-1}x,\;show\;that\;\sin(\cos^{-1}x)=x^2$

asked Jan 23, 2013 by meena.p

1 answer

Find the value of x if $cosec^{-1}x=2\cot^{-1}7+\cot^{-1}\frac{3}{4}$

asked Jan 23, 2013 by meena.p

1 answer

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

asked Jan 23, 2013 by meena.p

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

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