Find the simplified form of $\frac {1}{\cos x + \sin x}$ Find the simplified form of $\dfrac {1}{\cos x + \sin x}$.
a). $\dfrac {\sin (\dfrac {\pi}{4} +x)}{\sqrt {2}}$
b). $\dfrac {\csc (\dfrac {\pi}{4} + x)}{\sqrt {2}}$
c). $\dfrac {\sin (\dfrac {\pi}{4} + x)}{2}$
d). $\dfrac {\csc (\dfrac {\pi}{4} + x)}{2}$
My Attempt:
$$=\dfrac {1}{\cos x + \sin x}$$
$$=\dfrac {1}{\cos x + \sin x} \times \dfrac {\cos x - \sin x}{\cos x - \sin x}$$
$$=\dfrac {\cos x - \sin x}{\cos^2 x - \sin^2 x}$$
$$=\dfrac {\cos x - \sin x}{\cos 2x}$$

$$\frac{1}{\cos(x) + \sin(x)} = \frac{\sqrt2/2}{\sqrt2/2*\cos(x) + \sqrt2/2*\sin(x)} = \frac{\sqrt2/2}{\sin(\pi/4+x)} = \frac{\csc(\pi/4 + x)}{\sqrt2}$$
