1)sina + sin 3a + sin 5acosa + cos 3a + cos 5a

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вопрос

The given expression can be written as:

sina + sin 3a + sin 5a + cosa + cos 3a + cos 5a

We know that sin(x) + cos(x) = sqrt(2) * sin(x + pi/4)

Therefore, we can rewrite the expression using this identity:

sina + sin 3a + sin 5a + cosa + cos 3a + cos 5a

= sqrt(2) sin(a + pi/4) + sqrt(2) sin(3a + pi/4) + sqrt(2) * sin(5a + pi/4)

= sqrt(2) * (sin(a + pi/4) + sin(3a + pi/4) + sin(5a + pi/4))

So, the simplified expression is sqrt(2) * (sin(a + pi/4) + sin(3a + pi/4) + sin(5a + pi/4)).