Evaluate the following limit : lim(x→0) (tan 8x)/(sin 2x)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 0}\cfrac{tan\,8\text x}{sin\,2\text x} \)

lim(x→0) (tan 8x)/(sin 2x)

Answer 1

To find: \(\lim\limits_{\text x \to 0}\cfrac{tan\,8\text x}{sin\,2\text x} \)

\(\lim\limits_{\text x \to 0}\cfrac{tan\,8\text x}{sin\,2\text x} \)

Multiplying and Dividing by 8x in numerator & Multiplying and Dividing by 2x in the denominator:

As, x → 0 ⇒ 8x → 0 & 2x → 0

Now, put 2x = y and 8x = t

Formula used:

= 4

Hence, the value of \(\lim\limits_{\text x \to 0}\cfrac{tan\,8\text x}{sin\,2\text x} \) = 4