Question

Which is the expressions is equivalent to the expression 1/2 cos(4 theta)-(1/2)cos(8 theta)?

Answer 1

`sin(6\theta)sin(2\theta)`

Explanation:

We are given that an expression

`(1)/(2)cos(4\theta)-(1)/(2)cos(8\theta)`

The expression can be written as

`(1)/(2)(cos(4\theta)-cos(8\theta))`

`(1)/(2)(-2 sin ((4\theta+8\theta)/(2))sin((4\theta-8\theta)/(2)))`

Using identity:
`cos A-cos B=-2 sin((A+B)/(2))sin((A-B)/(2))`

`-sin(6\theta)sin(-2\theta)`

We know that

`Sin(-x)=-Sin x`

By using this property

We get

`sin(6\theta)sin(2\theta)`