Write the expression as the sine, cosine, or tangent of an angle. sin 5x cos x - cos 5x sin x

sin 5x cos x - cos 5x sin x = sin (4x)

Step-by-step explanation:

Given that the trigonometric expression,

sin 5x cos x - cos 5x sin x

Here we use the "sum and difference formulas"

Sum and Difference Formulas

sin (A+B) = sin A cos B + cos A sin B

sin (A-B) = sin A cos B - cos A sin B

cos (A+B) = cos A cos B - sin A sin B

cos (A-B) = cos A cos B + sin A sin B

So,

sin 5x cos x - cos 5x sin x = sin (5x - x)

sin 5x cos x - cos 5x sin x = sin (4x)

That's the final answer.