limits - Compute $limlimits_{xto0} left(sin x + cos xright)^{1/x}$

I hit a snag while solving exponential functions whose limits are given.

Question:

$$\lim_{x\to0} \left(\sin x + \cos x\right)^\left(1/x\right)$$

My Approach:

I am using the followin relation to solve the question of these type.

$$\lim_{x\to0} \left(1 + x\right)^\left(1/x\right) = e \qquad(2)$$

But now how should i convert my above question so that i can apply the rule as mentioned in $(2)$.

Conclusion:

First of all help will be appreciated.

Second how to solve functions of such kind in a quick method.

Thanks,

P.S.(Feel free to edit my question if you find any errors or mistakes in my question)

Answer

In this case the best idea is take logarithm, and then use De l'Hopital. $$\lim_{x \to 0} \frac{\ln (\sin x + \cos x)}{x} = \lim_{x \to 0} \frac{\cos x - \sin x}{\sin x + \cos x} = 1$$ Hence the answer is $e^{1}=e$.