the expression [tex]8sin7xcos4x[/tex] as a sum or difference is [tex]4(sin(7x+4x)+sin(7x-4x))[/tex] and , is simplified as [tex]4sin11x+4sin3x[/tex] .
Step-by-step explanation:
We need to rewrite the expression as a sum or difference , them simplify if possible , And the expression is : [tex]8sin7xcos4x[/tex]
From trigonometric identity we know that
[tex]2sinAcosB = sin(A+B)+sin(A-B)[/tex]
Using the above identity we get:
⇒ [tex]8sin7xcos4x[/tex]
⇒ [tex]4(2sin7xcos4x)[/tex]
⇒ [tex]4(sin(7x+4x)+sin(7x-4x))[/tex]
⇒ [tex]4(sin(11x)+sin(3x))[/tex]
⇒ [tex]4sin11x+4sin3x[/tex]
Therefore , the expression [tex]8sin7xcos4x[/tex] as a sum or difference is [tex]4(sin(7x+4x)+sin(7x-4x))[/tex] and , is simplified as [tex]4sin11x+4sin3x[/tex] .
