How do you prove $1- [(cos^(2)x)/(1+sinx)]= sinx$ ?

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Answer 1 · 2015-04-15T12:29:44

By the Pythagorean Theorem
$cos^2(x) + sin^2(x) = 1$
or
$cos^2(x) = 1-sin^2(x)$

So
$1-[(cos^2(x))/(1+sin(x))]$

$= 1- [(1-sin^2(x))/(1+sin(x))]$

$=1 - [((1-sin(x))*(1+sin(x)))/(1+sin(x))]$

$= 1- [1-sin(x)]$

$= sin(x)$

How do you prove 1- [(cos^(2)x)/(1+sinx)]= sinx1- [(cos^(2)x)/(1+sinx)]= sinx?