Question

Which expression is equivalent to sin(0.6x) - sin (0.4x) ?

Answer 1

The answer is  the first one  A

Answer 2

Answer:

$Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)$

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

Now Using formula.

$Sin (0.6x) - Sin (0.4x) = 2 cos (\frac{0.6x+0.4x}{2}) Sin (\frac{0.6x-0.4x}{2})$

$Sin (0.6x) - Sin (0.4x) = 2 cos (\frac{1x}{2}) Sin (\frac{0.2x}{2})$

$Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)$

Hence  $Sin (0.6x) - Sin (0.4x) = 2 cos (0.5x) Sin (0.1x)$

So, Option B is true.