Question

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

• A. $-\pi$
• B. $1$
• C. $-1$
• D. $\pi$

Answer 1

Answer: (D)

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