Question

The value of $\left[{lim}_{x\to \infty }(\frac{1}{sinx}-\frac{1}{tanx})\right]$ is :

• A. 0
• B. 1
• C. 2
• D. doesn't exist

Answer 1

The correct option is D doesn't exist

${lim}_{x\to \infty }(\frac{1}{sinx}-\frac{1}{tanx})={lim}_{x\to \infty }\left(\frac{1-cosx}{sinx}\right)$

$={lim}_{x\to \infty }\frac{2si{n}^2\frac{x}{2}}{2sin\frac{x}{2}cos\frac{x}{2}}$

= ${lim}_{x\to \infty }tan\frac{x}{2}=Does{n}^{\prime }texist$