Question

express sin 5x-sin 4x as a product of trigonometrc function

Answer 1

2 × cos((9x)/2) × sin((x)/2)

Answer 2

Answer:

$\sin 5x-\sin 4x=2\cos(\frac{9x}{2})\sin(\frac{x}{2})$

Step-by-step explanation:

The given expression is sin 5x-sin 4x.

Using the relation

$\sin C-\sin D=2\cos(\frac{C+D}{2})\sin(\frac{C-D}{2})$

On comparing, we get

C = 5x, D= 4x

Applying the formula

$\sin 5x-\sin 4x=2\cos(\frac{5x+4x}{2})\sin(\frac{5x-4x}{2})$

On simplifying, we get

$\sin 5x-\sin 4x=2\cos(\frac{9x}{2})\sin(\frac{x}{2})$