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