Respuesta :
Given:
The given expression is [tex]sin (2x) \ cos (5x) - sin (5x) \ cos (2x)[/tex]
We need to determine the simplified value of the given expression.
Simplification:
Since, the given expression is in the form of [tex]sin a \ cos b-\cos a \ sin b[/tex], the given expression can be simplified using the identity [tex]\sin (a-b)=\sin a \cos b-\cos a \sin b[/tex]
Comparing the given expression with the identity, we get;
[tex]a=2x[/tex] and [tex]b=5x[/tex]
Using this in the identity, we get;
[tex]sin (2x) \ cos (5x) - sin (5x) \ cos (2x)=sin(2x-5x)[/tex]
Simplifying, we get;
[tex]sin (2x) \ cos (5x) - sin (5x) \ cos (2x)=sin(-3x)[/tex]
Thus, the simplified value of the given expression is [tex]sin (-3x)[/tex]
Hence, Option c is the correct answer.
