Recent questions tagged p5

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 $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$

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

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

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 $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3.$

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

Show that the relation $R$ in $R$ defined as $R = {(a, b) : a \leq b} $, is reflexive and  transitive but not symmetric.

asked Nov 7, 2012 by vaishali.a

1 answer

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Show that the relation $R$ in the set $R$ of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Ask Questions, Get Answers

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

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

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

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

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 $x^{2006}+y^{2007}+z^{2008}-\Large \frac{9}{x^{2006}+y^{2007}+z^{2008}}$

Prove that $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$

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

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 $x$.

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

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

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

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

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

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

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

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

Show that the relation \(R\) in \(R\) defined as \(R = {(a, b) : a \leq b} \), is reflexive and  transitive but not symmetric.

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

Show that the relation \(R\) in the set \(R\) of real numbers, defined as $(R) =\{(a, b: (a \leq b^2 )\}$ is neither reflexive nor symmetric nor transitive.