Question #79582

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Answer 1 · 2016-10-30T22:06:23

This is just a trig question to get the solution into a different form;

Recall the sine addition formula:

# sin (A+ B) =sinAcosB + cosAsinB #

Put # A=B # to get a double angle formula;

# sin (A+ A) =sinAcosA + cosAsinA #
# :. sin (2A) =2sinAcosA #

If we put #A=2x# then;
# :. sin (2(2x)) =2sin2xcos2x #
# :. sin 4x =2sin2xcos2x #

Hence, # sin2xcos2x = 1/2sin 4x #