Question

Evaluate: ${lim}_{x\to \pi }\frac{{\sin }^{2}x+{\cos }^{2}x}{{\sin }^{2}x-{\cos }^{2}x}$

Answer 1

$li{m}_{x\to \pi }\frac{si{n}^{2}x+co{s}^{2}x}{si{n}^{2}x-co{s}^{2}x}$ substituting for numerator and denominator, the above equation takes the form,

$li{m}_{x\to \pi }\frac{1}{-cos2x}$, where $cos2x=co{s}^{2}x-si{n}^{2}x$

=$\frac{1}{-cos2\pi }=-1$