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which expression is equivalent to sin(0.6x) - sin (0.4x) ?
A.) 2cos(0.5x) sin(0.1x)
B.) 2cos(0.5x) cos(0.1x)
C.) 2sin(0.5x) sin(0.1x)
D.) -2sin(0.5x)sin(0.1x)
E.) -2cos(0.5x) sin(0.1x)

Respuesta :

The answer is  the first one  A

Answer:

[tex]Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)[/tex]

Step-by-step explanation:

Given :sin(0.6x) - sin (0.4x)

To Find: which expression is equivalent to sin(0.6x) - sin (0.4x)

Solution:

Formula : [tex]Sin a- Sin b = 2 cos (\frac{a+b}{2}) Sin (\frac{a-b}{2})[/tex]

Now Using formula.

[tex]Sin (0.6x) - Sin (0.4x) = 2 cos (\frac{0.6x+0.4x}{2}) Sin (\frac{0.6x-0.4x}{2})[/tex]

[tex]Sin (0.6x) - Sin (0.4x) = 2 cos (\frac{1x}{2}) Sin (\frac{0.2x}{2})[/tex]

[tex]Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)[/tex]

Hence  [tex]Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)[/tex]

So, Option B is true.

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