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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#