I think you're confusing sin(2x) with sin2(x)

You cannot treat trig functions like "sin" and "cos" as 
if they behaved like multication, because they don't!
To simplify trigonometric expressions and equations,
we us IDENTITIES:

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If the problem were as you solved it, you would
have had it half correct:



You would do as you did and factor out sin(x):



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Your solution of the second part here was incorrect.

HOWEVER, THIS IS NOT THE EQUATION YOU ARE TO SOLVE!!!

Here is the problem:



You cannot factor.

What you do is use the identity 



Now you can factor out sin(x)



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Edwin