Answer:
[tex]sin(6\theta)sin(2\theta)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{1}{2}cos(4\theta)-\frac{1}{2}cos(8\theta)[/tex]
The expression can be written as
[tex]\frac{1}{2}(cos(4\theta)-cos(8\theta))[/tex]
[tex]\frac{1}{2}(-2 sin (\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2}))[/tex]
Using identity: [tex] cos A-cos B=-2 sin(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
[tex]-sin(6\theta)sin(-2\theta)[/tex]
We know that
[tex] Sin(-x)=-Sin x[/tex]
By using this property
We get
[tex]sin(6\theta)sin(2\theta)[/tex]
