Please help Pre-Calc
1.Write the expression as the sine, cosine, or tangent of an angle.
sin 8x cos x - cos 8x sin x
2.Rewrite with only sin x and cos x.
cos 2x - sin x

Question

Please help Pre-Calc
1.Write the expression as the sine, cosine, or tangent of an angle.
sin 8x cos x - cos 8x sin x
2.Rewrite with only sin x and cos x. 
cos 2x - sin x

anonymous · Answer

looks like the "subtraction angle formula" for sine

anonymous · Answer

so how would I do it? Can you please show me the step by step process of how to do it?

anonymous · Answer

$$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$$ put $A=8x,B=x$ and go from the right side to the left side

anonymous · Answer

actually there is not much to do
you get 
$$\sin(8x-x)=\sin(7x)$$ and you are done

anonymous · Answer

So would the second question be cos2x + sin2x +sinx?