[ 2 ^ - 1 ( 1 5 ) - 4 ] = - Vidyadip

MCQ

$\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = $

A
$\frac{{17}}{7}$
B
$ - \frac{{17}}{7}$
C
$\frac{7}{{17}}$
✓
$ - \frac{7}{{17}}$

✓

Answer

Correct option: D.

$ - \frac{7}{{17}}$

d
(d) $\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = \tan \left[ {{{\tan }^{ - 1}}\frac{{\frac{2}{5}}}{{1 - \frac{1}{{25}}}} - {{\tan }^{ - 1}}(1)} \right]$

$ = \tan \left[ {{{\tan }^{ - 1}}\frac{5}{{12}} - {{\tan }^{ - 1}}(1)} \right] = \tan {\tan ^{ - 1}}\left( {\frac{{\frac{5}{{12}} - 1}}{{1 + \frac{5}{{12}}}}} \right) = - \frac{7}{{17}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 2. inverse trigonometric function→STD 12 - 2. inverse trigonometric function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int\frac{\sin\text{x}}{3+4\cos^2\text{x}}\text{ dx}=$

If $\text{x}=\text{f}(\text{t})\cos\text{t}-\text{f}(\text{t})\sin\text{t}\ \text{and}\ \text{y}=\text{f}(\text{t})\sin\text{t}+\text{f}(\text{t})\cos\text{t},$ then $\Big(\frac{\text{dx}}{\text{dt}}\Big)^2+\Big(\frac{\text{dy}}{\text{dt}}\Big)^2=$

Which of the following equation is non-linear

If $y=e^{-x}$, then $\frac{d^2 y}{d x^2}$ is equal to

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are any three mutualy perpendicular vectors of equal magnitude a, then $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|$ is equal to

The value of $‘a’$ in order that $f(x) = \sqrt 3 $ $\sin x - \cos x - 2ax + b$ decreases for all real values of $x$, is given by

vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are inclined at angle $\theta=120^\circ.$ if $|\vec{\text{a}}|=1,\big|\vec{\text{b}}\big|=2,$ then $\big[\big(\vec{\text{a}}+3\vec{\text{b}}\big)\times\big(3\vec{\text{a}}-\vec{\text{b}}\big)\big]^2$ is equal to:

If the position vectors of the points $A, B, C $ be $i + j,\,\,\,i - j$ and $a\,\,i + b\,j + c\,k$ respectively, then the points $A, B, C $ are collinear if

The point $B$ divides the arc $AC$ of a quadrant of a circle in the ratio $1 : 2$. If $O$ is the centre and $\overrightarrow {OA} = a$ and $\overrightarrow {OB} = b,$ then the vector $\overrightarrow {OC} $ is

What is the value of $x$ and $y,$ if $2i + 3j = xi + yj:$