The function $f(x) = \frac{1 - \sin{x + \cos x}}{1 + \sin{x + \cos x}}$ is not defined at$x = \pi$. The value of $f(\pi)$, so that $f(x)$ is continuous at $x = \pi$, is

Question

Dr. Abubacker · Accepted Answer

(c)
$\lim_{x ightarrow \pi}\ \frac{(1 + \cos{x) - \sin x}}{(1 + \cos{x) + \sin x}}\$
$= \lim_{x ightarrow \pi}\frac{2\cos^{2}{x/2 - 2(\sin{x/2)\ cos\ x/2}}}{2\cos^{2}{x/2 + 2(\sin{x/2)\ cos\ x/2}}}$
$= \lim_{x ightarrow \pi}	an{\left( \frac{\pi}{4} - \frac{\pi}{2} ight) = - 1}$
Since, $f(x)$ is continuous at $x = \pi$
$	herefore\ \ f(\pi) = \lim_{x ightarrow \pi}\ f(x) = - 1$

Q. The function $f(x) = \frac{1 - \sin{x + \cos x}}{1 + \sin{x + \cos x}}$ is not defined at$x = \pi$. The value of $f(\pi)$, so that $f(x)$ is continuous at $x = \pi$, is

Explanation

Reviewed by Dr. Abubacker

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