Question 138826
1)


*[Tex \LARGE \sin\left(7\theta\right)\cos\left(5\theta\right)] Start with the given expression



*[Tex \LARGE \frac{1}{2}\left(\sin\left(7\theta+5\theta\right)+\sin\left(7\theta-5\theta\right)\right) ] Use the Product-to-Sum formula



*[Tex \LARGE \frac{1}{2}\left(\sin\left(12\theta\right)+\sin\left(2\theta\right)\right) ] Add/Subtract



*[Tex \LARGE \frac{1}{2}\sin\left(12\theta\right)+\frac{1}{2}\sin\left(2\theta\right) ] Distribute




So *[Tex \LARGE \sin\left(7\theta\right)\cos\left(5\theta\right)=\frac{1}{2}\sin\left(12\theta\right)+\frac{1}{2}\sin\left(2\theta\right) ] 



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2)


Are you sure that it's {{{cos(7x)-sin(5x) }}}? There are no corresponding sum-to-product identities for mixed the trig functions sine and cosine.


Double check your assignment.