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