Question

Solve $\underset{x\to \frac{x}{2}}{lim}\frac{1-{\sin }^{3}x}{{\cos }^{2}x}$

• A. $\frac{1}{2}$
• B. $1$
• C. $0$
• D. None of these

Answer 1

The correct option is A $\frac{1}{2}$

Let $L={lim}_{x\to \frac{\pi }{2}}\frac{1-{\sin }^{3}x}{{\cos }^{2}x}=\frac{0}{0}$ form.

L- Hospital rule

$L={lim}_{x\to \frac{\pi }{2}}\frac{-3si{n}^{2}x.cosx}{-2cosxsinx}$

$={lim}_{x\to \frac{\pi }{2}}\frac{sinx}{2}$

$L=\frac{1}{2}$