How to solve? sin(5θ) − sin(−θ)

Question

Write the following sum as a product.

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Answer 1 · 2018-04-25T07:00:03

#sin5theta-sin(-theta)=2sin3thetacos2theta#

As #sin(-theta)=-sintheta#

#sin5theta-sin(-theta)#

= #sin5theta-(-sintheta)#

= #sin5theta+sintheta#

Now as #sinA+sinB=2sin((A+B)/2)cos((A-B)/2)#

we can write #sin5theta+sintheta# as

#2sin((5theta+theta)/2)cos((5theta-theta)/2)#

= #2sin3thetacos2theta#