Question

Express the sum or difference as a product. sin 4x - sin 6x

Answer 1

Answer:

sin 4x - sin 6x  = -2 cos 5x . sin x

Step-by-step explanation

We use the following result to solve this expression,

$sin\,A-sin\,B=2\,cos\,(\frac{A+B}{2})\,sin\,(\frac{A-B}{2})$

and sin(-x) = -sin x

Consider,

sin 4x - sin 6x

$=2\,cos\,(\frac{4x+6x}{2})\,sin\,(\frac{4x-6x}{2})$

$=2\,cos\,(\frac{10x}{2})\,sin\,(\frac{-2x}{2})$

$=2\,cos\,5x\,sin\,(-x)$

$=2\,cos\,5x\,(-sin\,x)$

$=-2\,cos\,5x\,sin\,x$

Therefore, sin 4x - sin 6x  = -2 cos 5x . sin x

Answer 2

Hello,

Since:
$sin (a)- sin(b)=cos( \frac{a+b}{2}) sin( \frac{a-b}{2} )\\ sin(4x)-sin(6x)=-(sin(6x)-sin(4x))=-2 cos(5x) sin(x)$