[ 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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}$ is exactly $33,$ then the least value of $n$ is

The sum $1^2-2.3^2+3.5^2-4.7^2+5.9^2-\ldots +15.29^2$ is $.......$.

Let $A , B , C$ be $3 \times 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric.Consider the statements

$(S1): A ^{13} B ^{26}- B ^{26} A ^{13}$ is symmetric

$(S2):A ^{26} C ^{13}- C ^{13} A ^{26}$ is symmetric

Then,

Considering only the principal values of the inverse trigonometric functions, the value of

$\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is. . . .

Let $f(x) = \left\{ \begin{array}{l}{x^p}\sin \frac{1}{x},x \ne 0\\0\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x = 0\end{array} \right.$ then $f(x)$ is continuous but not differential at $x = 0$ if

The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$, is

If the system of equations $x +y + z = 6$ ; $x + 2y + 3z= 10$ ; $x + 2y + \lambda z = 0$ has a unique solution, then $\lambda $ is not equal to

Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is

The length of tangent from the point $(5, 1)$ to the circle ${x^2} + {y^2} + 6x - 4y - 3 = 0$, is

Two mutually perpendicular straight lines through the origin from an isosceles triangle with the line $2x + y = 5$ . Then the area of the triangle is :