How do you use the sum to product formulas to write the sum or difference #sinx+sin5x# as a product?

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Answer 1 · 2017-01-19T17:45:48

The answer is #=2sin3xcos2x#

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

#sin(A-B)=sinAcosB-sinBcosA#

Adding the 2 equations

#sin(A+B)+sin(A-B)=2sinAcosB#

Here, we have

#A+B=5x#

and #A-B=x#

Therefore,

#2A=6x#, #=>#, #A=3x#

and #B=2x#

so,

#sinx+sin5x=2sin3xcos2x#