Evaluate the following limit : lim(x→0) (sec 5x - sec 3x)/(sec 3x - sec x)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sec\,5\text x-sec\,3\text x}{sec\,3\text x-sec\,\text x} \)

lim(x→0) (sec 5x - sec 3x)/(sec 3x - sec x)

Answer 1

To find: \(\lim\limits_{\text x \to0}\cfrac{sec\,5\text x-sec\,3\text x}{sec\,3\text x-sec\,\text x} \)

We know,

= 2

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sec\,5\text x-sec\,3\text x}{sec\,3\text x-sec\,\text x} \) = 2