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The cosine of pi/2 is 0 so the problem really says "find the angle between - pi/2 and pi/2 whose tan = 0. That would be the same as asking for the angle whose sin is 0. That would be 0.

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Answer:

The angle is 0°.

Step-by-step explanation:

Consider the provided trigonometric function.

\(tan^{-1}(cos\frac{\pi}{2})\)

The given interval \([\frac{-\pi}{2}, \frac{\pi}{2}]\)

The value of \(cos\frac{\pi}{2}=0\)

Now substitute the respective value in the provided trigonometric function.

\(tan^{-1}(tan(0))=0\) by inverse property of trigonometric function

Hence, the angle is 0°.

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