If ( ^ - 1 x)^2 + ( ^ - 1 x)^2 = 5 ^2 8 , then x equals - Vidyadip

MCQ

If ${({\tan ^{ - 1}}x)^2} + {({\cot ^{ - 1}}x)^2} = \frac{{5{\pi ^2}}}{8},$ then $x$ equals

✓
$-1$
B
$1$
C
$0$
D
None of these

✓

Answer

Correct option: A.

$-1$

a
(a) ${({\tan ^{ - 1}}x)^2} + {({\cot ^{ - 1}}x)^2} = \frac{{5{\pi ^2}}}{8}$

==> ${({\tan ^{ - 1}}x + {\cot ^{ - 1}}x)^2} - 2{\tan ^{ - 1}}x\left( {\frac{\pi }{2} - {{\tan }^{ - 1}}x} \right) = \frac{{5{\pi ^2}}}{8}$

==> $\frac{{{\pi ^2}}}{4} - 2 \times \frac{\pi }{2}{\tan ^{ - 1}}x + 2{({\tan ^{ - 1}}x)^2} = \frac{{5{\pi ^2}}}{8}$

==> $2{({\tan ^{ - 1}}x)^2} - \pi {\tan ^{ - 1}}x - \frac{{3{\pi ^2}}}{8} = 0$

==> ${\tan ^{ - 1}}x = - \frac{\pi }{4},\frac{{3\pi }}{4}$

==> ${\tan ^{ - 1}}x = - \frac{\pi }{4} \Rightarrow x = - 1$.

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

If in a $\triangle\text{ABC}$, $\text{A}=(0,0),\ \text{B}=(3,3\sqrt3),\ \text{C}=(-3\sqrt3,3)$, then the vecctor of magnitude $2\sqrt2$ units directed along AO, where O is the circumcenter of $\triangle\text{ABC}$ is,

The value of $\int\limits_0^{\pi /2} {\frac{{{{\sin }^3}\,x}}{{\sin \,x\, + \,\cos \,x}}} \,dx$ is

If a random variable $X$ follows the Binomial distribution $B (33, p )$ such that $3 P ( X =0)= P ( X =1)$, then the value of $\frac{ P ( X =15)}{ P ( X =18)}-\frac{ P ( X =16)}{ P ( X =17)}$ is equal to

If $\vec{\text{a}}.\hat{\text{i}}=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}\big)=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)=1.$then $\vec{\text{a}}=$

Forces $3\overrightarrow{\text{OA}},\ 5\overrightarrow{\text{OB}}$ act along $OA$ and $OB$. If their resultant passes through $C$ on $AB,$ then,

If three points $A, B$ and $C$ have position vectors $\hat{\text{i}}+\text{x}\hat{\text{j}}+3\hat{\text{k}},\ 3\hat{\text{i}}+4\hat{\text{j}}+7\hat{\text{k}}$ and $\text{y}\hat{\text{i}}-2\hat{\text{j}}-5\hat{\text{k}}$ respectively are collinear, then $(x, y) =$

Choose the correct answer from the given four options.
The distance of the plane $\vec{\text{r}}\Big(\frac{2}{7}\hat{\text{i}}+\frac{3}{7}\hat{\text{j}}-\frac{6}{7}\hat{\text{k}}\Big)=1$ from the origin is:

If $y=\sin ^{-1} x$, then $\left(1-x^2\right) y_2$ is equal to

Let $[x]$ be the greatest integer less than or equals to $x$. Then, at which of the following point($s$) the function $f(x)=x \cos (\pi(x+[x]))$ is discontinuous?

$[A]$ $x=-1$ $[B]$ $x=0$ $[C]$ $x=2$ $[D] x=1$

The value of $\cot \left( {\sum\limits_{n = 1}^{19} {{{\cot }^{ - 1}}\left( {1 + \sum\limits_{p = 1}^n {2p} } \right)} } \right)$ is