Sin 2p/15 cos p/5 + cos 2p/15 sin p/5

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вопрос

To simplify the given expression, we can use the following trigonometric identity:

sin(A + B) = sinA cosB + cosA sinB

Applying the identity to the given expression:

2p/15 cos p/5 + cos 2p/15 sin p/5
= sin(2p/15 + p/5)

Now we need to find a common denominator for the angles inside the sine function:
2p/15 and p/5

The common denominator for 15 and 5 is 15, so we need to multiply p/5 by 3/3 to make the denominators 15. We then get:
= sin(6p/15 + 3p/15)
= sin(9p/15)
= sin(3p/5)

Therefore, the simplified expression is sin(3p/5).