Recent questions tagged medium

Prove the following: \[ 2 \: tan^{-1} \frac{1}{2} + tan ^{-1} \frac{1}{7} = tan^{-1} \frac{31}{17} \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \frac{\sqrt {1 + x^2} - 1}{x}, x \neq 0\]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \frac{1}{\sqrt{x^2 - 1}}, | x | > 1 \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form: \[ tan^{-1} \bigg( \frac{cos\: x - sin\: x}{cos\: x + sin\: x} \bigg) , 0 < x < \pi \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form:\[ tan^{-1} \bigg( \frac{3a^2x-x^3}{a^3-3ax^2} \bigg), a > 0 ; \frac{-a}{\sqrt 3} \leq x \leq \frac{a}{\sqrt 3} \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the value of $ \tan^{-1} \bigg[ 2\cos \bigg(2\sin^{-1}\frac{1}{2}\bigg) \bigg] $

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the value of \[ tan\frac{1}{2} \bigg[ sin^{-1} \frac{2x}{1+x^2} + cos^{-1} \frac{1-y^2}{1+y^2} \bigg], | x | < 1, y > 0 \: and \: xy < 1\]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

If $ \tan^{-1} \frac{\large x-1}{\large x-2} + \tan^{-1} \frac{\large x+1}{\large x+2} = \frac{\large \pi}{\large 4} $ then find the value of $x$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the values of the expression $ \tan \bigg( \sin^{-1} \frac{3}{5} + \cot^{-1} \frac{3}{2} \bigg) $

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Let $f:\;N\;\to N\;be\;defined\;by\;f(n)= \left\{ \begin{array}{1 1} \frac{n+1}{2}, & if\;n\;is\;odd\\ \frac{n}{2}, & if\;is\;even\end{array} \right. \qquad for\;all\;n \in N$ \[\text{state whether the function f is bijective.Justify your answer.} \]

asked Dec 10, 2012 by sreemathi.v

1 answer

What does $ 2\sin^{-1} \frac{3}{5}$ reduce to

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Find the scalar and vector components of the vector with initial point $(2, 1)$ and terminal point $(– 5, 7).$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the vector $ \hat i + \hat j + \hat k$ is equally inclined to the axes OX, OY and OZ.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $ \hat i + 2\hat j − \hat k$ and $ – \hat i + \hat j + \hat k$ respectively, in the ratio $2 : 1$ internally

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the points A, B and C with position vectors, $ \overrightarrow a = 3\hat i − 4\hat j − 4\hat k, \overrightarrow b = 2\hat i − \hat j + \hat k$ and $ \overrightarrow c = \hat i − 3\hat j − 5\hat k$ , respectively form the vertices of a right angled triangle.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int(4\;e^{3x}+1)\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integral $\int\sqrt x\;(3x^2+2x+3)\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integral $\large \int \frac{\sec^2x}{\large cosec^2x}$$dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

If the vertices $A, B, C$ of a triangle $ABC$ are $(1, 2, 3), (-1, 0, 0), (0, 1, 2)$ respectively, then find $ \angle ABC. \angle ABC$ is the angle between the vectors $ \overline {BA}$ and $\overline {BC}$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $\frac{\large 1}{\large x-\sqrt x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Show that the vectors $2\hat i - \hat j + \hat k, \: \hat i - 3\hat j - 5\hat k$ and $3\hat i - 4\hat j - 4\hat k$ form the vertices of a right angled triangle.

asked Dec 6, 2012 by thanvigandhi_1

1 answer