How do you simplify the expression $\frac{{sin}^{2} x}{1 + cos x}$ $sin^2x/(1+cosx)$ ?

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Answer 1 · 2016-11-27T12:35:39

The answer is $= 1 - cos x$ $=1-cosx$

We use

${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$

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

Therefore,

$sin^2x/(1+cosx)=(cancel(1+cosx)(1-cosx))/cancel(1+cosx)$

$=1-cosx$

How do you simplify the expression sin^2x/(1+cosx)sin2x1+cosxsin^2x/(1+cosx)?