The value of ^ -1 ( 3 2 )+2 ^ -1 ( 3 2 ) : - Vidyadip

Question

The value of $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)+2 \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ :

✓

Answer

(C)
The range of principal value branch of $\sin ^{-1} x$ is $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$ and the range of principal value branch of $\cos ^{-1} x$ is $[0, \pi]$.
$\therefore \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{3}$ and $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{6}$
Hence, $\frac{\pi}{3}+2 \times \frac{\pi}{6}=\frac{\pi}{3}+\frac{\pi}{3}=\frac{2 \pi}{3}$
Hence correct option is (C)

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The direction cosines of the y-axis are:

The direction coisines of the y-axis are:

If X follows a binomial distribution with parameter $\text{n}=8$ and $\text{p}=\frac{1}{2},$ then $\text{P(|X}-4|\leq2)$ equals:

$\frac{118}{128}$
$\frac{119}{128}$
$\frac{117}{128}$
$\text{None of these}$

If from Lagrange's mean value theorem, we have
$\text{f}'(\text{x}_1)=\frac{\text{f}(\text{b})-\text{f}(\text{a})}{\text{b}-\text{a}},$ then:

Find the principal values of: $\operatorname{cosec}^{-1}(2)$

Evaluate: $\int\frac{1}{1+3\sin^2\text{x}+8\cos^2\text{x}}\text{dx}.$

$\frac{1}{6}\tan^{-1}(2\tan\text{x})+\text{c}$
$\tan^{-1}(2\tan\text{x})+\text{c}$
$\frac{1}{6}\tan^{-1}(\frac{2\tan\text{x}}{3})+\text{c}$
$\text{None of these}$

If $\beta$ is perpendicular to both $\alpha$ and $\gamma$, where $\alpha=\hat{k}$ and $\gamma=\gamma=2 \hat{i}+3 \hat{j}+4 \hat{k}$, then what is $\beta$ equal to?

If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}+\overrightarrow{\text{OD}}=$

$2\overrightarrow{\text{OG}}$
$4\overrightarrow{\text{OG}}$
$5\overrightarrow{\text{OG}}$
$3\overrightarrow{\text{OG}}$

The function $f : R \rightarrow R$ given by $f(x) = x^3 – 1$ is:

The vector equation of the plane containing the line $\vec{\text{r}}=(-2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}})+\lambda(3\hat{\text{i}}-2\hat{\text{j}}-\hat{\text{k}})$ and the point $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ is:

$\vec{\text{r}}.(\hat{\text{i}}+3\hat{\text{k}})=10$
$\vec{\text{r}}.(\hat{\text{i}}-3\hat{\text{k}})=10$
$\vec{\text{r}}.(3\hat{\text{i}}+\hat{\text{k}})=10$
$\text{None of these}$