Question

Sin(x)×sin(120-x)×sin(120+x)

Answer 1

Answer:

the answer is

$\frac{1}{4} \sin(3x)$

Step-by-step explanation:

the answer is explained in the image.

Answer 2

$\huge \underline \bold \color{teal} \mathfrak{Answer }$

$\sin(x) \sin(120 - x) \sin(120 + x)$

Multiplying and dividing by 2

$\frac{ \sin(x) }{2} (2 \sin(120 - x) \sin(120 + x) )$

Using the formula 2 sin A sin B = cos(A-B) - cos(A+B), we get

$\ \frac{ \sin(x) }{2} ( \cos( - 2x) - \cos(240) )$

Since cos(-A) =cos A and cos 240 = - 1/2

$\frac{ \sin(x) }{2} ( \cos(2x) + \frac{1}{2} )$

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

Multiplying and dividing by 2.

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

Using the formula 2 sin A cos B = sin(A+B) +sin(A-B)

$\frac{ \sin(3x) - \sin(x) + \sin(x) }{4}$

$\huge \color{green} \frac{ \sin(3x) }{4}$

Hope it helps.....

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