Question

Cos бэта sin5 бэта -sin бэта cos5 бэта

Answer 1

cosB sin5B - sinB cos5B = sin (5B-B) = sin4B

Answer 2

To simplify the expression "cos β sin^5 β - sin β cos^5 β," we can use the trigonometric identity:

sin(α - β) = sin α cos β - cos α sin β.

Now, let's identify the values of α and β in our expression:

α = 5β β = β

So, sin(α - β) becomes sin(5β - β). Substituting this back into the original expression:

cos β sin^5 β - sin β cos^5 β = sin(5β - β).

Now, we simplify the expression inside the sine function:

5β - β = 4β.

The final simplified expression is:

cos β sin^5 β - sin β cos^5 β = sin(4β).