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How do you simplify $2tanxcos^2x$ ?

1 Answer

Nov 20, 2015

$2tan(x)cos^2(x) = sin(2x)$

Explanation:

$tan(x) = sin(x)/cos(x)$

So
$color(white)("XXX")2tan(x)cos^2(x)$

$color(white)("XXX") = 2sin(x)/cancel(cos(x))*cancel(cos(x))*cos(x)$

$color(white)("XXX") = 2sin(x)cos(x)$

which by the Double Angle Formula for Sines
$color(white)("XXX")=sin(2x)$

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