Recent questions tagged ch2

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

asked Feb 19, 2013 by sreemathi.v

1 answer

Find the value of $tan^{-1}\frac{-1}{\sqrt 3}+cot^{-1}\frac{1}{\sqrt 3}-tan^{-1}sin\frac{\pi}{2}$

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

Solve : \[ tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\frac{8}{31}\]

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Prove that $\bigg( tan \bigg( \frac{\pi}{4}+\frac{1}{2} cos^{-1}\frac{a}{b} \bigg)+tan \bigg(\frac{\pi}{4}-\frac{1}{2} cos^{-1}\frac{a}{b} \bigg) = \frac{2b}{a} \bigg)$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Prove that : \[ 2tan^{-1} \bigg( \frac{1}{2} \bigg) + tan^{-1} \bigg( \frac{1}{7} \bigg) = tan^{-1} \bigg( \frac{31}{17} \bigg) \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Solve the following for x : \[ tan^{-1} \bigg( \frac{x-1}{x-2} \bigg) + tan^{-1} \bigg( \frac{x+1}{x+2} \bigg) = \frac{\pi}{4} \]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find principal value of the expression $ cos^{-1}(cos(-680^{\circ})).$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Prove that $ tan^{-1}\sqrt x = \frac{1}{2}cos^{-1} \bigg(\frac{1-x}{1+x} \bigg), x \in [0,1].$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve the equation $ sin^{-1}6x+sin^{-1}6\sqrt 3 x = -\frac{\pi}{2}. $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the values of x which satisfy the equation \[ sin^{-1}x+sin^{-1}(1-x)=cos^{-1}x.\]

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove that $ 2sin^{-1}\frac{3}{5}-tan^{-1}\frac{17}{31}=\frac{\pi}{4} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

What is the principal value of $ \cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg). $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove that $ \tan^{-1} \large\frac{63}{16}=\sin^{-1}\bigg( \large\frac{5}{13} \bigg) + \cos^{-1} \bigg( \large\frac{3}{5} \bigg). $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove the following : $\large\frac{9\pi}{8}-\frac{9}{4}sin^{-1}\bigg(\large\frac{1}{3} \bigg) = \frac{9}{4}sin^{-1}\bigg(\large \frac{2\sqrt 2}{3} \bigg) $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Solve the following equation for x : $ \tan^{-1} \bigg( \large\frac{1-x}{1+x} \bigg) = \large\frac{1}{2}\tan^{-1}(x), x > 0 $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Prove the following : $ \tan^{-1} \bigg(\large\frac{1}{2} \bigg) + \tan^{-1} \bigg( \large\frac{1}{5} \bigg) + \tan^{-1} \bigg( \frac{1}{8} \bigg)=\large\frac{\pi}{4} $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Prove the following : $ \cot^{-1} \bigg[ \large\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}} \bigg] = \frac{x}{2}, x \in \bigg( 0, \frac{\pi}{4} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the value of $ \tan{-1} \bigg(\large \frac{x}{y} \bigg)-\tan^{-1} \bigg(\large \frac{x-y}{x+y} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Solve $ \tan^{-1}(x+1)+tan^{-1}(x-1)=tan^{-1}\large\frac{8}{31} $.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Solve for x : $ 2\tan^{-1}(\sin x)=\tan^{-1} (2\sec x),0 < x < \large\frac{\pi}{2} $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Show that : $ \tan\large\frac{1}{2} \bigg[ \sin^{-1}\frac{2x}{1+x^2} + \cos^{-1}\large\frac{1-y^2}{1+y^2} \bigg] =\large \frac{x+y}{1-xy}$$, |x| < 1, y > 0 \: xy < 1 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Simplify : $ \cos^{-1} \bigg(\large \frac{3}{5}$$ \cos \theta +\large \frac{4}{5}$$ sin \theta \bigg) $

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Solve : $ \tan^{-1}2x+tan^{-1}3x = \large\frac{\pi}{4}. $

asked Feb 2, 2013 by thanvigandhi_1

1 answer

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

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Show that $ \sin^{-1}\large\frac{12}{13}$$+\cos^{-1}\large\frac{4}{5}$$+\tan^{-1}\large\frac{63}{16} $$= \pi $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Prove that $ 2\tan^{-1} \large\frac{1}{5}$$ + \tan^{-1} \large\frac{1}{8}$$ = \tan^{-1}\large \frac{4}{7} $

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \tan^{-1} \bigg(\large \frac{x-1}{x+1} \bigg) + \tan^{-1} \bigg( \frac{2x-1}{2x+1} \bigg) = \tan^{-1} \bigg( \frac{23}{36} \bigg). $

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Prove that $ \tan^{-1} \large\frac{1}{7}$$ + 2\tan^{-1} \large\frac{1}{3} = \frac{\pi}{4} $

asked Jan 24, 2013 by thanvigandhi_1

1 answer

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

If $ \tan^{-1}a+\tan^{-1}b+\tan^{-1}c=\pi,\;prove\;that\;a+b+c=abc.$

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

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

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