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

The expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x) and this can be determined by using the trigonometric properties.

Given :

Expression  --  (sin 3x - sin x)

The following steps can be used in order to determine the expression equivalent to (sin 3x - sin x):

Step 1 - The trigonometric properties can be used in order to determine the expression equivalent to (sin 3x - sin x).

Step 2 - Below are the properties that help to evaluate the given expression.

$\rm sin \;A - sin\;B = 2cos\left(\dfrac{A+B}{2}\right) sin\left(\dfrac{A-B}{2}\right)$

Step 3 - Use the above-mentioned property in the given expression.

$\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{3x+x}{2}\right) sin\left(\dfrac{3x-x}{2}\right)$

$\rm sin \;3x - sin \; x = 2 cos\left(\dfrac{4x}{2}\right) sin\left(\dfrac{2x}{2}\right)$

$\rm sin \;3x - sin \; x = 2 cos\left(2x\right) sin\left(x\right)$

So, the expression equivalent to (sin 3x-sin x) is 2cos(2x)sin(x).

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https://brainly.com/question/24236629