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Answer 1 · 2017-01-03T03:23:48

Please see explanation below.

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

$(1/cosx)/((sinx/cosx)+(cosx/sinx))=sinx$

rewrite denominator

$(1/cosx)/((sin^2x+cos^2x)/(cosxsinx))=sinx$

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

$(1/cosx)/(1/(cosxsinx))=sinx$

We rewrite the fraction as follows

$(1/cosx)(cosxsinx)/1$

The $cosx$ cancels and we are left with

$sinx=sinx$