Asked on by sfrasier13

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve, use the product to sum identities which is:

`sin A + sin B= 2sin((A+B)/2)cos((A-B)/2)`

Applying the identity, the left side of the equation becomes:




To simplify the equation further, apply the double angle identity of sine which is sin(2A)=2sinAcosA.



Since cos(-x) = cosx, then the left side becomes:



Dividing both sides by 4, the equation simplifies to:


Then, set each factor equal to zero and solve for x.

For the first factor:


`x=0,pi, 2pi`

For the second factor:



`x=pi/2, (3pi)/2`

Hence, `x = 0, pi/2, pi, (3pi)/2` and `2pi` .

Since there is no indicated interval for x, the solution should be express in general form.

Therefore, the solution to the given equation is

`x = pik`



where k is any integer.

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