Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]=$
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{4}$
  • ✓
    $\frac{\pi}{3}$
✓

Answer

Correct option: D.
$\frac{\pi}{3}$
We have, $\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]$
$=\cos ^{-1}\left[\cos 2\left(\frac{\pi}{6}\right)\right]$
$=\cos ^{-1}\left(\cos \left(\frac{\pi}{3}\right)\right)=\cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}$

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 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

Out of the given matrices, choose that matrix which is a scalar matrix:
→
Which of the following is not a convex set?
→
If $\alpha=\tan^{-1}\Big(\tan\frac{5\pi}{4}\Big)$ and $\beta=\tan^{-1}\Big(-\tan\frac{2\pi}{3}\Big),$ then:
→
Let $\text{f(x)}=\frac{\alpha\text{x}}{\text{x}+1},\ \text{x}\neq-1.$ Then, for what value of $\alpha$ is $f(f(x)) = x?$
→
Let the matrix $A$ and $B$ be defined as $A\, = \,\left[ {\begin{array}{*{20}{c}}
  3&2 \\ 
  2&1 
\end{array}} \right]$ and $B\, = \,\left[ {\begin{array}{*{20}{c}}
  3&1 \\ 
  7&3 
\end{array}} \right]$ , then the value of $det. \,(2A^9B^{-1}),$ is :-
→
The system of vectors i, j, k is:
→
$\sin\big[\cot^{-1}\big\{\tan\big(\cos^{-1}\text{x}\big)\big\}\big]$ is equal to:
→
Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then The function $ f (x)$
→
The area bounded by the curve $y = x^2 + 1\,$ and the tangents to it drawn from the origin is
→
Construct a $3 \times 2$ matrix whose elements are given by   $a_{i j}=\frac{1}{2}|i-3 j|$.
→