Answer:
\(\sin (9x)\cos (x) - \cos 9(x) \sin (x)=\sin (8x)\)
Step-by-step explanation:
Given : Expression \(\sin (9x)\cos (x) - \cos 9(x) \sin (x)\)
To find : Write the expression as the sine, cosine, or tangent of an angle?
Solution :
We know the trigonometry property of additional,
\(\sin A\cos B-\cos A\sin B=\sin (A-B)\)
On comparing the expression with property,
A=9x and B=x
Substitute in formula,
\(\sin (9x)\cos (x) - \cos 9(x) \sin (x)=\sin (9x-x)\)
\(\sin (9x)\cos (x) - \cos 9(x) \sin (x)=\sin (8x)\)
Therefore, The expression is written as the sine of an angle
\(\sin (9x)\cos (x) - \cos 9(x) \sin (x)=\sin (8x)\)
