Question #366e9

2 Answers
turksvids
Feb 2, 2018

#sin(10theta)+sin(4theta)#

Explanation:

start with the sum and difference formulas for sine:
#sin(a+b)=sin(a)cos(b)+cos(a)sin(b)#
#sin(a-b)=sin(a)cos(b)-cos(a)sin(b)#

add them together to get:

#sin(a+b)+sin(a-b)=2sin(a)cos(b)#

For this problem, let #a=7theta# and #b=3theta#, so

#2sin(7theta)cos(3theta)=sin(7theta+3theta)+sin(7theta-3theta)#
#=sin(10theta)+sin(4theta)#

Jim G.
Feb 2, 2018

#sin10theta+sin4theta#

Explanation:

#"using the "color(blue)"product to sum formula"#

#•color(white)(x)2sinAcosB=sin(A+B)+sin(A-B)#

#"here "A=7theta" and "B=3theta#

#rArr2sin7thetacos3theta#

#=sin(7theta+3theta)+sin(7theta-3theta)#

#=sin10theta+sin4theta#

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