Given:
[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]
To find:
The correct equivalent equation.
Solution:
We have,
[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]
Taking sin on both sides, we get
[tex]\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A[/tex]
[tex]\dfrac{5}{8}=\sin A[/tex] [tex][\because \sin (\sin^{-1}\theta )=\theta][/tex]
Interchanging the sides, we get
[tex]\sin A=\dfrac{5}{8}[/tex]
Therefore, the correct option is 4.
