Question #b2380

Dec 10, 2016

$sin(x)+sin(7x)=2sin(4x)cos(3x)$

Using the formula

$sin(alpha)+sin(beta) = 2sin((alpha+beta)/2)cos((alpha-beta)/2)$

we have

$sin(x)+sin(7x) = 2sin((x+7x)/2)cos((x-7x)/2)$

$=2sin((8x)/2)cos(-(6x)/2)$

$=2sin(4x)cos(-3x)$

$=2sin(4x)cos(3x)$

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