Write the value of 3 - ^ -1 (-1 2 ) . - Vidyadip

Question

Write the value of $\sin\Big\{\frac{\pi}{3}-\sin^{-1}\Big(-\frac{1}{2}\Big)\Big\}.$

✓

Answer

$\sin\Big\{\frac{\pi}{3}-\sin^{-1}\Big(-\frac{1}{2}\Big)\Big\}$
$=\sin\Big\{\frac{\pi}{3}+\sin^{-1}\Big(\frac{1}{2}\Big)\Big\}$ $\big\{\text{Since},\sin^{-1}(-\theta)=-\sin^{-1}\theta\big\}$
$=\sin\Big\{\frac{\pi}{3}+\frac{\pi}{6}\Big\}$ $\Big\{\text{Since},\sin^{-1}\text{x}=\text{An angle in}\Big[-\frac{\pi}{2},\frac{\pi}{2}\Big]\text{whose sine is x}\Big\}$
$=\sin\Big(\frac{\pi}{2}\Big)$
$=1$
Hence,
$\sin\Big\{\frac{\pi}{3}-\sin^{-1}\Big(-\frac{1}{2}\Big)\Big\}=1$

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

Explore more

More "3 Marks Question" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\frac{2\text{x}^4+7\text{x}^3+6\text{x}^2}{\text{x}^2+2\text{x}}\text{dx}$

Using determinants show that the following points are collinear:
(2, 3), (-1, -2) and (5, 8)

Find the unit vector in the direction of sum of vectors $\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{j}}+\hat{\text{k}}.$

Find gof and fog when $f : R \rightarrow R$ and $g : R \rightarrow R$ are defined by:
$f(x) = 2x + 3$ and $g(x) = x^2 + 5$

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum?

Evaluate the following integrals:
$\int5^{\text{x}+\tan^{-1}\text{x}}.\Big(\frac{\text{x}^2+2}{\text{x}^2+1}\Big)\text{dx}$

A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three non-coplanar vectors, such that $\vec{\text{d}}.\vec{\text{a}}=\vec{\text{d}}.\vec{\text{b}}=\vec{\text{d}}.\vec{\text{c}}=0,$ then show that $\vec{\text{d}}$ is the null vector.

Prove that the relation R in the set $\text{A } = (1, 2, 3, 4, 5)$ given by $\text{R} = (\text{a, b)} : |\text{a-b|} \text{is even},$ is an equivalence relation.