Answer:
D
Step-by-step explanation:
1. Remind that
[tex]\tan \left(\dfrac{\pi }{4}\right)=1.[/tex]
Here you can use trigonometric table to find the value of [tex]\tan\left(\dfrac{\pi}{4}\right)[/tex], or you can remind that [tex]\dfrac{\pi}{4}=45^{\circ}[/tex] and [tex]\tan45^{\circ}=1[/tex] because special right triangle 45°-45°-90° is isosceles (with congruent oppposite and adjacent legs) and the ratio between the opposite leg and adjacent leg is equal to 1.
2. Now
[tex]\sin^{-1}\left(\tan\left(\dfrac{\pi}{4}\right)\right)=\sin^{-1}1=\dfrac{\pi}{2},[/tex]
because
[tex]\sin\dfrac{\pi}{2}=1.[/tex]
