Question

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)

Answer 1

The answer is  the first one  A

Answer 2

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

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 ((a+b)/(2)) Sin ((a-b)/(2))`

Now Using formula.

`Sin (0.6x) - Sin (0.4x) = 2 cos ((0.6x+0.4x)/(2)) Sin ((0.6x-0.4x)/(2))`

`Sin (0.6x) - Sin (0.4x) = 2 cos ((1x)/(2)) Sin ((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.