Find the value of cos(sin⁻¹3/√2) is

The correct option is 1/2.

Let us find the value of the given trigonometric expression step-by-step. Note that the term in the question, "cos(sin⁻¹3/√2)", is a standard representation of the expression:
$$\cos \left({\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)$$

Step 1: Simplify the inner inverse trigonometric function
Let us set the inner term equal to an angle, θ:
$$\theta ={\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$$
By definition of the inverse sine function, this is equivalent to:
$$\sin \left(\theta \right)=\frac{\sqrt{3}}{2}$$
Since the principal value range of ${\sin }^{-1}\left(x\right)$ is $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$, we find the angle θ that satisfies this:
$$\theta =\frac{\pi }{3}\text{ (or }60°\text{)}$$

Step 2: Substitute the angle back into the outer function
Now we substitute θ back into the original cosine expression:
$$\cos \left({\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)=\cos \left(\theta \right)$$
Substitute the value of θ:
$$\cos \left(\frac{\pi }{3}\right)=\frac{1}{2}$$
Therefore, the final value is 1/2.