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Recent questions tagged inverse-trignometric-properties

Find all positive integral solutions of the equation $\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$

asked Nov 18, 2013 by sreemathi.v

1 answer

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

asked Nov 15, 2013 by sreemathi.v

1 answer

If $-\large\frac{x}{2}$$<\sin^{-1}x<\large\frac{x}{2}$ then $\tan(\sin^{-1}x)$ is equal to

asked Nov 15, 2013 by sreemathi.v

1 answer

If $\tan^{-1}\big(\large\frac{a}{x}\big)$$+\tan^{-1}\big(\large\frac{b}{x}\big)=\frac{\pi}{2}$ then $x$ is equal to

asked Nov 15, 2013 by sreemathi.v

1 answer

If $\tan^{-1}\large\frac{1}{a-1}$$=\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ is

asked Nov 15, 2013 by sreemathi.v

1 answer

Find all possible values of $p$ and $q$ for which $\cos^{-1}\sqrt p+\cos^{-1}\sqrt{1-p}=\large\frac{3\pi}{4}$

asked Oct 21, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be positive real numbers .Let $\theta=\tan^{-1}\sqrt{\large\frac{a(a+b+c)}{bc}}+$$\tan^{-1}\sqrt{\large\frac{b(a+b+c)}{ca}}$$+\tan^{-1}\sqrt{\large\frac{c(a+b+c)}{ab}}$.Then $\tan\theta$

asked Oct 21, 2013 by sreemathi.v

1 answer

Evaluate : $\sin^{-1}\large\frac{4}{5}$$+\sin^{-1}\large\frac{5}{13}$$+\sin^{-1}\large\frac{16}{65}$

asked Oct 17, 2013 by sreemathi.v

1 answer

Find the value of $\tan\big[\large\frac{1}{2}$$\big(\sin^{-1}\large\frac{2x}{1+x^2}+$$\cos^{-1}\large\frac{1-y^2}{1+y^2}\big)\big],$$\mid x\mid < 1,y > 0$ and $xy <1$

asked Oct 17, 2013 by sreemathi.v

1 answer

Evaluate : $\tan\big[\large\frac{1}{2}$$\cos^{-1}\large\frac{\sqrt 5}{3}\big]$

asked Oct 17, 2013 by sreemathi.v

1 answer

$\cot^{-1}\big(\sqrt{\cos\alpha}-\tan^{-1}(\sqrt{\cos\alpha}\big)=x$ then $\sin x=?$

asked Oct 16, 2013 by sreemathi.v

1 answer

Find $\cos\tan^{-1}\sin\cot^{-1}x$

asked Oct 16, 2013 by sreemathi.v

1 answer

The value of $\cot\sum\limits_{n=1}^{23}\cot^{-1}\big(1+\sum\limits_{k=1}^n 2k\big)$ is

asked Oct 16, 2013 by sreemathi.v

1 answer

The number of real solutions of $\tan^{-1}\sqrt{x(x+1)}+\sin^{-1}\sqrt{x^2+x+1}=\large\frac{\pi}{2}$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

If $x_1=2\tan^{-1}\big(\large\frac{1+x}{1-x}\big)$$,x_2=\sin^{-1}\big[\large\frac{1-x^2}{1+x^2}\big]$ where $x\in(0,1)$ then $x_1+x_2$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

If $\cot(\cos^{-1}x)=\sec\big[\tan^{-1}\large\frac{a}{\sqrt{b^2-a^2}}\big]$ then $x$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

If $a=\sin^{-1}\big(\large\frac{-1}{\sqrt 2}\big)+$$\cos^{-1}\big(\large\frac{-1}{2}\big),$$b=\tan^{-1}\big(-\sqrt 3\big)-\cot^{-1}\big(-\large\frac{1}{\sqrt 3}\big)$ then

asked Oct 11, 2013 by sreemathi.v

1 answer

A solution of $\sin^{-1}(1)-\sin^{-1}\big(\large\frac{\sqrt 3}{x^2}\big)$$-\large\frac{\pi}{6}$$=0$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

The value of $x$ satisfying $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ are

asked Oct 11, 2013 by sreemathi.v

1 answer

If $\sin^{-1}x+\sin^{-1}y=\large\frac{\pi}{2}$ then $\cos^{-1}x+\cos^{-1}y$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

The principal value of $\sin^{-1}\tan\big(\large\frac{-5\pi}{4}\big)$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

The value of $\cot (cosec^{-1}\large\frac{5}{3}$$+\tan^{-1}\large\frac{2}{3})$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

Find the value of $\cos[2\cos^{-1}x+\sin^{-1}x]$ at $x=\large\frac{1}{5}$ where $0\leq \cos^{-1} x\leq \pi$ and $\large\frac{-\pi}{2}$$\leq \sin^{-1}x\leq \large\frac{\pi}{2}$

asked Oct 10, 2013 by sreemathi.v

1 answer

The value of $\tan\bigg[\cos^{-1}\big(\large\frac{4}{5}\big)$$+\tan^{-1}\big(\large\frac{2}{3}\big)\bigg]$ is

asked Oct 9, 2013 by sreemathi.v

1 answer

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