Question

Rewrite the expression as a sum or difference, then simplify if possible.

Answer 1

the expression
`8sin7xcos4x` as a sum or difference is
`4(sin(7x+4x)+sin(7x-4x))` and , is simplified as
`4sin11x+4sin3x` .

Explanation:

We need to rewrite the expression as a sum or difference , them simplify if possible , And the expression is :
`8sin7xcos4x`

From trigonometric identity we know that

`2sinAcosB = sin(A+B)+sin(A-B)`

Using the above identity we get:

⇒
`8sin7xcos4x`

⇒
`4(2sin7xcos4x)`

⇒
`4(sin(7x+4x)+sin(7x-4x))`

⇒
`4(sin(11x)+sin(3x))`

⇒
`4sin11x+4sin3x`

Therefore , the expression
`8sin7xcos4x` as a sum or difference is
`4(sin(7x+4x)+sin(7x-4x))` and , is simplified as
`4sin11x+4sin3x` .