Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Find the principal values of: $\sec ^{-1}(2)$
  • A
    $\frac{\pi}{6}$
  • ✓
    $\frac{\pi}{3}$
  • C
    $\frac{2 \pi}{3}$
  • D
    $\frac{5 \pi}{6}$
✓

Answer

Correct option: B.
$\frac{\pi}{3}$
(b) : Let $\sec ^{-1}(2)=\theta \Rightarrow \sec \theta=2=\sec \frac{\pi}{3}$
$\Rightarrow \theta=\frac{\pi}{3} \in[0, \pi]-\left\{\frac{\pi}{2}\right\}$
$\therefore \quad$ Principal value of $\sec ^{-1}(2)$ is $\frac{\pi}{3}$.

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 Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Area bounded between the curve $x^2=y$ and the line $y=4 x$ is:
→
The solution of the equation $\frac{{{x^2}{d^2}y}}{{d{x^2}}} = \ln x,$ when $x = 1$, $y = 0$ and $\frac{{dy}}{{dx}} = - 1$ is
→
Let $r$ be a relation from $R$ (set of real numbers) to $R$ defined by $r = \{(a,b) \, | a,b \in R$  and  $a - b + \sqrt 3$ is an irrational number$\}$ The relation $r$ is
→
$\int_{}^{} {\frac{{dx}}{{{e^x} + {e^{ - x}}}} = } $
→
Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail, is
→
If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=1,|\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=\sqrt{3}$, then the angle between $2 \vec{a}$ and $-\vec{b}$ is:
→
If $a, b, c$  are mutually perpendicular unit vectors, then $|a + b + c|\,\, = $
→
Let $A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right], \quad$ where $x, y$ and $z$ are real numbers such that $x + y + z >0$ and $xyz =2$ If $A ^{2}= I _{3},$ then the value of $x ^{3}+ y ^{3}+ z ^{3}$ is ............
→
The real number  $x $ when added to its inverse gives the minimum value of the sum at $ x$ equal to
→
$\int\cos(\log_\text{e}.\text{x})\text{dx}$ is equal to:
→