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

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Answer 1 · 2016-05-09T02:02:39

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

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

Applying the Pythagorean identity $sin^2x + cos^2x = 1$ :

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

$1/cosx$

Applying the reciprocal identity $1/cosx = secx$ :

$secx$

Hopefully this helps!

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