Given:
The expression is
[tex]arcsine\left(\dfrac{\sqrt{2}}{2}\right)[/tex]
To find:
The value of given expression.
Solution:
We have,
[tex]arcsine\left(\dfrac{\sqrt{2}}{2}\right)[/tex]
It can be rewritten as
[tex]=\sin^{-1}\left(\dfrac{\sqrt{2}}{2}\right)[/tex]
[tex]=\sin^{-1}\left(\dfrac{1}{\sqrt{2}}\right)[/tex]
[tex]=\sin^{-1}\left(\sin \dfrac{\pi}{4}}\right)[/tex]
[tex]=\dfrac{\pi}{4}[/tex]
Therefore, the correct option is B.
