Write the product as a sum or difference.
6cos(21t)sin(20t)
select the correct answer below:

3cos(t)−3cos(41t)

3sin(41t)−3sin(t)

3sin(t)−3cos(41t)

3cos(41t)−3sin(t)

3cos(41t)+3cos(t)

3sin(41t)+3sin(t)

3 sin(41t) - 3 sin(t)

Step-by-step explanation:

The general formula to convert the product of the form cos(a)sin(b) into sum is:

cos(a) sin(b) = 0.5 [ sin(a+b) - sin (a-b) ]

The given product is:

6 cos(21t) sin(20t) = 6 [ cos(21t) sin(20t) ]

Comparing the given product with general product mentioned above, we get:

a = 21t and b = 20t

Using these values in the formula we get:

6 cos(21t) sin(20t) = 6 x 0.5 [ sin(21t+20t) - sin(21t-20t)]

= 3 [sin(41t) - sin(t)]

= 3 sin(41t) - 3 sin(t)

Therefore, second option gives the correct answer