^ -1 ( 1+3 3+3 )+ ^ -1 ( 8+4 3 6+3 3 ) is equal to ......... - Vidyadip

MCQ

$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
✓
$\frac{\pi}{3}$
D
$\frac{\pi}{6}$

✓

Answer

Correct option: C.

$\frac{\pi}{3}$

c
$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$

$=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)=\frac{\pi}{3}$

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 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]$, then determinant of ${A^2} - 2A$ is

Let $\vec{a}$ and $\vec{b}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{a}+\vec{b}$ is a unit vector if $\theta =$

The vectors $2\,i + 3\,j - 4\,k$ and $a\,i + b\,j + c\,k$ are perpendicular, when

If O and O' are circumcenter and orthocenter of $\triangle{\text{ABC}}$ , then $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}$ equals,

$2\overrightarrow{\text{OO}'}$
$\overrightarrow{\text{OO}'}$
$\overrightarrow{\text{O}'\text{O}}$
$2\overrightarrow{\text{O}'\text{O}}$

If $f(x)$ = $\left\{ \begin{gathered}
\frac{{a + 3\cos x}}{{{x^2}}},\,\,\,\,\,\,\,\,\,x < 0 \hfill \\
b\,\tan \left( {\frac{\pi }{{\left[ {x + 3} \right]}}} \right),\,x \geqslant 0 \hfill \\
\end{gathered} \right.$ is continuous at $x = 0$ , then

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is:

720
120
0
None of these.

Let $A = \left[ {\begin{array}{*{20}{c}}1&2\\3&4\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}a&0\\0&b\end{array}} \right]\;,a,b \in N$ then

$\int_{}^{} {\frac{{3\cos x + 3\sin x}}{{4\sin x + 5\cos x}}\;dx = } $

Given two independent events, if the probability that exactly one of them occurs is $\frac {26}{49}$ and the probability that none of them occurs is $\frac {15}{49}$ , then the probability of more probable of the two events is

For square matrix A if $A = B +\frac{ C }{2}$, where B is skew symmetric matrix and C is symmetric matrix, then C = _________.