How do you simplify the expression $sinx/cosx+cosx/(1+sinx)$ ?

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Answer 1 · 2016-09-01T05:11:08

$sec x$ .

$"The Expression"=sin x/cos x + cos x/(1+sin x)$

$={(sin x)(1+sin x)+cos^2 x}/{(cos x)(1+sin x)}$

$=(sin x+sin^2 x+cos^2 x)/{(cos x)(1+sin x)}$

$=cancel(sin x+1)/(cos x cancel((1+sin x))$

$=1/cos x$

$=sec x$ .

How do you simplify the expression sinx/cosx+cosx/(1+sinx)sinx/cosx+cosx/(1+sinx)?