Question

The function $f\left(x\right)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$ is not defined at $x=\pi$. If $f\left(x\right)$ is continuous at $x=\pi$, then the value of $f\left(\pi \right)$ is

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

Answer 1

Answer: (A)

$-1$

$f\left(x\right)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$

Applying L-hospital rule to the function

$=\frac{0-\cos x-\sin x}{0+\cos x-\sin x}$

$f(x=\pi )=\frac{0-\cos \pi -\sin \pi }{0+\cos \pi -\sin \pi }$

$=\frac{0+1-0}{0-1-0}$

$=-1$

$\therefore f\left(\pi \right)=-1$