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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:
For the second factor:
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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