Question

The expression equivalent to sin 3x−sin x is what

Answer 1

Answer:

The required equivalent form of given expression is

$\sin 3x-\sin x=2\cos 2x\sin x$

Step-by-step explanation:

Given : Expression $\sin 3x-\sin x$

To find : The expression is equivalent to ?

Solution :

Applying trigonometric formula,

$\sin a - \sin b = 2\cos(\frac{a+b}{2})\sin(\frac{a-b}{2})$

where, a=3x and b=x

$\sin 3x-\sin x=2\cos(\frac{3x+x}{2})\sin(\frac{3x-x}{2})$

$\sin 3x-\sin x=2\cos(\frac{4x}{2})\sin(\frac{2x}{2})$

$\sin 3x-\sin x=2\cos 2x\sin x$

Therefore, The required equivalent form of given expression is

$\sin 3x-\sin x=2\cos 2x\sin x$

Answer 2

This can be written as a product.

sin3x - sin x  = 2 cos(3+1)x  sin (3 - 1)x
                                   ------          --------    = 2 cos  2x sin x
                                     2                  2