Question
Evaluate : $\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$

Answer

$\text { (d) }: \sin \left(\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right)$
$=\sin \left(\frac{\pi}{3}+\frac{\pi}{6}\right)=\sin \frac{\pi}{2}=1$

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

Similar questions

Find the shortest distance between the given two lines :
$\frac{x+1}{1}=\frac{y+1}{-1}=\frac{z+1}{1}$ and $\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{4}$.
A linear programming of linear functions deals with:
Choose the correct answer from given four options in each of the Exercise$:$
The value of $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{a}\\\text{b}-\text{a}&\text{c}+\text{a}&\text{b}\\\text{c}-\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is:
$\int\limits^{2\text{a}}_0\text{f}(\text{x})\text{dx}$ is equal to:
  1. $2\int\limits^{\text{a}}_0\text{f(x)}\text{dx}$
  2. $0$
  3. $\int\limits^{\text{a}}_0\text{f}(\text{x})\text{dx}+\int\limits^{\text{a}}_0\text{f}(2\text{a}-\text{x})\text{dx}$
  4. $\int\limits^{\text{a}}_0\text{f}(\text{x})\text{dx}+\int\limits^{2\text{a}}_0\text{f}(2\text{a}-\text{x})\text{dx}$
Choose the correct answer from the given four options.
The value of $\cot\Big[\cos^{-1}\Big(\frac{7}{25}\Big)\Big]$ is:
  1. $\frac{25}{24}$
  2. $\frac{25}{7}$
  3. $\frac{24}{25}$
  4. $\frac{7}{24}$
Direction ratio of line joining (2, 3, 4) and (-1, -2, 1), are:
If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of n and r, then p equals:
$\int\frac{\text{x}^3}{\text{x}+1}\text{ dx}$ is equal to:
  1. $\text{x}+\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
  2. $\text{x}+\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
  3. $\text{x}-\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
  4. $\text{x}-\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is:
  1. $1$
  2. $\frac{\text{a}-1}{\text{a}}$
  3. $\frac{\text{a}}{\text{a}-1}$
  4. $0$
When the tangent to the curve $\text{y}=\text{x}\log\text{x}$ is parallel to the chord joining the points (1, 0) and (e, e), the value of x is:
  1. $\text{e}^{\frac{1}{1}-\text{e}}$
  2. $\text{e}^{(\text{e}-1)(2\text{e}-1)}$
  3. $\text{e}^{\frac{2\text{e}-1}{\text{e}-1}}$
  4. $\frac{\text{e}-1}{\text{e}}$