Question

${lim}_{x\to 0}\frac{sin\left(\pi co{s}^{2}x\right)}{x^2}$ equals

• A. $-\pi$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $1$

Answer 1

The correct option is B $\pi$

${lim}_{x\to 0}\frac{sin\left(\pi co{s}^{2}x\right)}{x^2}{lim}_{x\to 0}\frac{sin(\pi -\pi si{n}^{2}x)}{x^2}\left[sin\right(\pi -\theta )=sin\theta ]={lim}_{x\to 0}\frac{sin\left(\pi si{n}^{2}x\right)}{\pi si{n}^{2}x}\times \frac{\left(\pi si{n}^{2}x\right)}{x^2}=\pi$