How do you use the sum to product formulas to write the sum or difference #sin3theta+sintheta# as a product?

Question

3363 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-23T09:04:56

#2sin2thetacostheta=4sinthetacos^2theta#

The relevant sum to product formula

#color(blue)(sinX+sinY=2sin((X+Y)/2)cos((X-Y)/2))#

we have

#sin3theta+sintheta#

#X=3theta,Y=theta#

so

#sin3theta+sintheta=2sin((3theta+theta)/2)cos((3theta-theta)/2)#

#=2sin2thetacostheta#

if you required it as single angles

using

#color(red)(sin2theta=2sinthetacostheta)#

#=4sinthetacos^2theta#