Find the value of ^ -1 (2 (2 ^ -1 1 2 ) ). - Vidyadip

MCQ

Find the value of $\tan ^{-1}\left(2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right)$.

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

✓

Answer

Correct option: B.

$\frac{\pi}{4}$

(b) : We have,
$
\begin{array}{l}
\tan ^{-1}\left\{2 \cos \left(2 \sin ^{-1}\left(\frac{1}{2}\right)\right)\right\}=\tan ^{-1}\left\{2 \cos \left(2 \times \frac{\pi}{6}\right)\right\} \\
=\tan ^{-1}\left\{2 \cos \frac{\pi}{3}\right\}=\tan ^{-1}\left[2 \times \frac{1}{2}\right]=\tan ^{-1} 1=\frac{\pi}{4} \\
\end{array}
$

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

A family has 2 children and the elder child is a girl. The probability that both children are girls is:

Let $T$ be the tangent to the ellipse $E: x^{2}+4 y^{2}=5$ at the point $P(1,1)$. If the area of the region bounded by the tangent $T$, ellipse $E$, lines $x=1$ and $x=\sqrt{5}$ is $\alpha \sqrt{5}+\beta+\gamma \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)$, then $|\alpha+\beta+\gamma|$ is equal to $....$

If $f(x) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\sin x}}{x} + \cos x,} \, & \,when \,\, {x \ne 0} \\ {2,} \,& \,\,when\,\,{x = 0} \end{array}} \right.$ then

$\int_{}^{} {\frac{{dx}}{{\sin x + \cos x}}} = $

If $\text{A}=\begin{vmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}\end{vmatrix}$ and C_ij is cofactor of a_ij in a, then value of |A| is given by:

a₁₁C₃₁ + a₁₂C₃₂ + a₁₃C₃₃
a₁₁C₁₁ + a₁₂C₂₁ + a₁₃C₃₁
a₂₁C₁₁ + a₂₂C₁₂ + a₂₃C₁₃
a₁₁C₁₁ + a₂₁C₂₁ + a₁₃C₃₁

The direction cosines of the normal to the plane 2x - 3y - 6z - 3 = 0 are:

$\frac{2}{7},\frac{-3}{7},\frac{-6}{7}$
$\frac{2}{7},\frac{3}{7},\frac{6}{7}$
$\frac{-2}{7},\frac{-3}{7},\frac{-6}{7}$
None of these

The sum of two forces is $18\, N$ and resultant whose direction is at right angles to the smaller force is $12\,N.$ The magnitude of the two forces are

Let $h(x) = \min \{ x,\,{x^2}\} ,$ for every real number of $x$. Then

Maximize Z = 7x + 11y, subject to $3\text{x}+5\text{y}\leq26,5\text{x}+3\text{y}\leq30,\text{x}\geq0,\text{y}\geq0.$

59 at$\Big(\frac{9}{2},\frac{5}{2}\Big)$
42 at (6, 0)
49 at (7, 0)
57.2 at (0, 5.2)

If $a = 2i + 4j + 2k$ and $b = 8i - 3j + \lambda k$ and $a\, \bot \,b,$ then value of $\lambda $ will be