# Question #d1e3c

Dec 4, 2016

Put on a common denominator and use the identity $\sec \theta = \frac{1}{\cos} \theta$.

$\frac{\left(1 + \sin x\right) \left(1 + \sin x\right)}{\cos x \left(1 + \sin x\right)} + {\cos}^{2} \frac{x}{\cos x \left(1 + \sin x\right)} = \frac{2}{\cos} x$

Use the identity ${\sin}^{2} \theta + {\cos}^{2} \theta = 1$.

$\frac{1 + 2 \sin x + {\sin}^{2} x + {\cos}^{2} x}{\cos x + \cos x \sin x} = \frac{2}{\cos} x$

$\frac{1 + 2 \sin x + 1}{\cos x + \cos x \sin x} = \frac{2}{\cos} x$

$\frac{2 + 2 \sin x}{\cos x + \cos x \sin x} = \frac{2}{\cos} x$

$\frac{2 \left(1 + \sin x\right)}{\cos x \left(1 + \sin x\right)} = \frac{2}{\cos} x$

$\frac{2}{\cos} x = \frac{2}{\cos} x$

Hopefully this helps!