Question

The value of $\underset{x\to \pi }{\lim }\frac{sin\left(2\pi co{s}^{2}x\right)}{tan\left(\pi se{c}^{2}x\right)}$ is equal to

• A. $1$
• B. $2$
• C. $-2$
• D. $0$

Answer 1

Answer: (C)

$\underset{x\to \pi }{\lim }\frac{sin\left\{2\pi \left(1-si{n}^{2}x\right)\right\}}{tan\left\{\pi \left(1+ta{n}^{2}x\right)\right\}}=\underset{x\to \pi }{\lim }\frac{sin\left\{2\pi -2\pi si{n}^{2}x\right\}}{tan\left\{\pi +\pi ta{n}^{2}x\right\}}$
$=\underset{x\to \pi }{\lim }\frac{-sin\left\{2\pi si{n}^{2}x\right\}}{tan\left\{\pi ta{n}^{2}x\right\}}$
$=\underset{x\to \pi }{\lim }\frac{-sin\left\{2\pi {\left(sin\right)}^{2}x\right\}}{\left\{2\pi {\left(sin\right)}^{2}x\right\}}\times \frac{2\pi {\left(sin\right)}^{2}x}{\pi {\left(tan\right)}^{2}x}\times \frac{\pi {\left(tan\right)}^{2}x}{tan\left(\pi {\left(tan\right)}^{2}x\right)}$
$=-1\times 2\times 1=-2$