Question

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

Answer 1

Here is your answer
Hope it Helps

Answer 2

Answer:

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

Step-by-step explanation:

We need to express sin 5x - sin 4x as a product of trigonometric functions.

In order to get the required expression, we use the formula :

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

Here, in the above formula put A = 5x and B = 4x

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

Hence, This is the required form of the expression in which the given expression is expressed as a product of trigonometric functions.