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\displaystyle [br]\begin{align*}\sin x \tan x + \cos x &= \sin x\frac{\sin x}{\cos x} + \frac{\cos^2 x}{\cos x} \\ & = \frac{\sin^2 x + \cos^2 x}{\cos x} \\&= \frac{1}{\cos x} \end{align*}
\displaystyle [br]\begin{align*}\sin x \tan x + \cos x &= \sin x\frac{\sin x}{\cos x} + \frac{\cos^2 x}{\cos x} \\ & = \frac{\sin^2 x + \cos^2 x}{\cos x} \\&= \frac{1}{\cos x} \end{align*}
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