Question

Which expression is equivalent to cos(1.4x) - cos(0.6x)

a.) -2sinxsin(0.4x)
b.) 2sinxsin(0.4x)
c.) -2cosxcos(0.4x)
d.) 2cosxcox(0.4x)

Answer 1

cos(1.4x) = cos(x)cos(.4x) -sin(x)sin(.4x)
cos(0.6x) = cos(x)cos(.4x) +sin(x)sin(.4x)
The difference of these is
cos(1.4x) -cos(0.6x) = cos(x)cos(.4x) -sin(x)sin(.4x) -cos(x)cos(.4x) -sin(x)sin(.4x)
= -2sin(x)sin(.4x)

This matches the first selection, ...
a.) -2sin(x)·sin(0.4x)