Question 1138452
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Use these two identities
{{{cos(x+y) = cos(x)cos(y) - sin(x)sin(y)}}}
{{{cos(x-y) = cos(x)cos(y) + sin(x)sin(y)}}}


to say that,
{{{cos(x+y) - cos(x-y) = (cos(x)cos(y) - sin(x)sin(y)) - (cos(x)cos(y) + sin(x)sin(y))}}}


{{{cos(x+y) - cos(x-y) = cos(x)cos(y) - sin(x)sin(y) - cos(x)cos(y) - sin(x)sin(y)}}}


{{{cos(x+y) - cos(x-y) = (cos(x)cos(y) - cos(x)cos(y)) + (-sin(x)sin(y) - sin(x)sin(y))}}}


{{{cos(x+y) - cos(x-y) = (0) + (-2sin(x)sin(y))}}}


{{{cos(x+y) - cos(x-y) = -2sin(x)sin(y)}}}


The original expression simplifies to <font color=red size=4>-2sin(x)sin(y)</font>


{{{cos(x+y) - cos(x-y) = -2sin(x)sin(y)}}} is an identity. It is a true equation no matter what values of x and y you select. 
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