Evaluate the following limit : lim(x→π/2) (tan 2x)/(x - π/2)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to\pi/2}\cfrac{tan\,2\text x}{\text x-\frac\pi2} \)

lim(x→π/2) (tan 2x)/(x - π/2)

Answer 1

= \(\lim\limits_{\text x \to\pi/2}\cfrac{tan\,2\text x}{\text x-\frac\pi2} \)

lim(x→π/2) (tan 2x)/(x - π/2)

As x tends to π/2, x − π/2 tends to zero.

Let,