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Answer 1 · 2017-01-03T03:23:48

Please see explanation below.

Rewrite everything in terms of $sin (x)$ $sin(x)$ and $cos (x)$ $cos(x)$

$\frac{\frac{1}{cos x}}{(\frac{sin x}{cos x}) + (\frac{cos x}{sin x})} = sin x$ $(1/cosx)/((sinx/cosx)+(cosx/sinx))=sinx$

rewrite denominator

$\frac{\frac{1}{cos x}}{\frac{{sin}^{2} x + {cos}^{2} x}{cos x sin x}} = sin x$ $(1/cosx)/((sin^2x+cos^2x)/(cosxsinx))=sinx$

Note that ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$

$\frac{\frac{1}{cos x}}{\frac{1}{cos x sin x}} = sin x$ $(1/cosx)/(1/(cosxsinx))=sinx$

We rewrite the fraction as follows

$(\frac{1}{cos x}) \frac{cos x sin x}{1}$ $(1/cosx)(cosxsinx)/1$

The $cos x$ $cosx$ cancels and we are left with

$sin x = sin x$ $sinx=sinx$