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  $4sin11x+4sin3x$ .

Step-by-step 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  $4sin11x+4sin3x$ .