This question is taken from a very challenging calculus problems book called the Advanced Problems in Mathematics by Vikas Gupta
And I have absolutely no clue on how to approach questions of the kind. My initial thought since y is composite function was to check for a graph similar to the outermost function which is that of tan. Now option D looked compelling. But I was incorrect.
Then I decided to substitute values like say $x=\pi/4$ but that would yield $\tan(1/{\sqrt{2}})$ which is hard to compute.
So please do advise me on how to approach this question efficiently. Thanks