Evaluate $\tan \pi/2$

Hint: Here in this question we have been asked to evaluate the value of a given trigonometric function at a corresponding angle that is $\tan \dfrac{\pi }{2}$ . We know that the value of “$\pi$” is given as ${{180}^{\circ }}$ . We also know that the value of $\tan {{90}^{\circ }}$ is undefined.

Complete step by step answer:
Now considering from the question we have been asked to evaluate the value of the given trigonometric function at a corresponding angle that is $\tan \dfrac{\pi }{2}$ .
From the basic concepts we know that the value of “pi” is given as ${{180}^{\circ }}$ .
Now we will substitute this value in the given expression then we will have $\tan \dfrac{{{180}^{\circ }}}{2}=\tan {{90}^{\circ }}$ .
From the basic concepts of trigonometry, we have studied a trigonometric table containing the values of all the trigonometric functions corresponding to the specified values of angles. We know that the value of $\tan {{90}^{\circ }}$ is undefined

Hence we can conclude that the value of the given trigonometric function $\tan \dfrac{\pi }{2}$ is undefined.

Note: While answering questions of this type we should be careful with the trigonometric concepts that we are going to apply in the process. This is a very simple and easy question and can be answered in a short span of time. Very few mistakes are possible in questions of this type. If someone had forgotten the table and tried solving it using the tangent and sine and cosine relation they can make an error by assuming that $\tan \theta =\dfrac{\cos \theta }{\sin \theta }$ instead of $\tan \theta =\dfrac{\sin \theta }{\cos \theta }$ then they will end up having the result as 0 which is wrong answer.