How do I simplify the trigonometric expression? cos(x)/sec(x) + tan(x)

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Answer 1 · 2018-02-07T23:02:53

#cos^2x+tanx#

#cosx/secx+tanx#

Identity:

#color(red)bb(secx=1/cosx)#

#(cosx)/(1/cosx)+tanx#

#cos^2x+tanx#

Answer 2 · 2018-02-07T23:04:18

It can be simplified to #1 - sinx#

I will assume that the question asks #(cosx)/(secx + tanx)#

Using our fundamental identities of #secx = 1/cosx# and #tanx = sinx/cosx#, we will get:

#cosx/(1/cosx + sinx/cosx)#

#cosx/((1 + sinx)/cosx)#

#cos^2x/(1+ sinx)#

We know that #sin^2x + cos^2x =1#, therefore:

#(1 - sin^2x)/(1 + sinx)#

#((1 +sinx)(1 - sinx))/(1 + sinx)#

#1 - sinx#

Hopefully this helps!