Download App

STD 12 - 2. inverse trigonometric function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 2. inverse trigonometric function1 Mark
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 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 $f:R \to R$ satisfies $f(x + y) = f(x) + f(y)$, for all $x,\;y \in R$ and $f(1) = 7$, then $\sum\limits_{r = 1}^n {f(r)} $ is
→
The distance of the point $Q(0,2,-2)$ form the line passing through the point $\mathrm{P}(5,-4,3)$ and perpendicular to the lines $\overrightarrow{\mathrm{r}}=(-3 \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$ $\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}), \quad \lambda \in \mathbb{R} \quad$ and $\quad \overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+$ $\mu(-\hat{i}+3 \hat{J}+2 \hat{K}), \mu \in \mathbb{R}$ is
→
If $f(x)=4 x^8$, then :
→
Let $[t]$ denote the greatest integer less than or equal to $t.$ Then, the value of the integral $\int\limits_{0}^{1}\left[-8 x^{2}+6 x-1\right] d x$ is equal to
→
Let $\quad P_1=I=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right], \quad P_2=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right], \quad P_3=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right], \quad P_4=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right], \quad P_5=\left[\begin{array}{lll}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{array}\right]$,

$P_6=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right]$ and $X=\sum_{k=1}^6 P_k\left[\begin{array}{lll}2 & 1 & 3 \\ 1 & 0 & 2 \\ 3 & 2 & 1\end{array}\right] P_k^{\top}$

where $P _{ K }^{ T }$ denotes the transpose of the matrix $P _{ K }$. Then which of the following options is/are correct?

$(1)$ $X -30 I$ is an invertible matrix

$(2)$ The sum of diagonal entries of $X$ is 18

$(3)$ If $X \left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=\alpha\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$, then $\alpha=30$

$(4)$ $X$ is a symmetric matrix

→
Let $\text{f(x)}=|\sin\text{x}|.$ then,
→
If for the matrix $A, A^3=1$, than $A^{-1}=$
→
Evaluate : $\int_0^2 e^{3-4 x} d x$
→
Which of the following function  $(s)$ not defined at $x = 0$ has/have removable discontinuity at $x = 0$ ?
→
$\int {\frac{{{x^2}}}{{{x^2} + 4}}\,\,dx} $ equals to
→