Question

Evaluate $\underset{a\to 0}{lim}\frac{1+\sin x-\cos x}{1-\sin x-\cos x}$

Answer 1

$\underset{x\to 0}{lim}$ $\frac{1+\sin x-\cos x}{1-\sin x-\cos x}$

Using LHR

$\Rightarrow \frac{\cos x+\sin x}{-\cos x+\sin x}$

$\Rightarrow -\frac{1}{1}$

$\Rightarrow -1$