Answer:
[tex]\sin (8x)=\sin (9x) \cos (x) - \cos (9x)\sin (x)[/tex]
Step-by-step explanation:
Given : Expression [tex]\sin (9x) \cos (x) - \cos (9x)\sin (x)[/tex]
To write : The given expression as the sine, cosine, or tangent of an angle?
Solution :
The given expression is in the form [tex]\sin A\cos B-\cos A \sin B[/tex]
Using trigonometric identity,
[tex]\sin (A-B)=\sin A\cos B-\cos A \sin B[/tex]
Substituting, A=9x , B=x
[tex]\sin (9x-x)=\sin (9x) \cos (x) - \cos (9x)\sin (x)[/tex]
[tex]\sin (8x)=\sin (9x) \cos (x) - \cos (9x)\sin (x)[/tex]
Therefore, The given expression is in the sin form sin(8x).
