Question

Question #366e9

Answer 1

`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)`

Answer 2

`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`