Cos(4theta)sin(2theta)+sin(3theta)cos(theta)=sin(5theta)cos(theta)?

1 Answer
Abhishek K.
Jul 10, 2018

Let #theta=x# then

#LHS=cos4xsin2x+sin3xcosx#

#=1/2[2cos4xsin2x+2sin3xcosx]#

#=1/2[sin(4x+2x)-sin(4x-2x)+sin(3x+x)+sin(3x-x)]#

#=1/2[sin6xcancel(-sin2x)+sin4xcancel(+sin2x)]#

#=1/2[2sin((6x+4x)/2)cos((6x-4x)/2)]#

#=sin5xcosx=RHS#

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