2cos(x+п/4)cos(2x+п/4)+sin3x -упростить

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вопрос

2cos(x+π/4)cos(2x+π/4) + sin3x

Using the double angle formula for cosine:
2cos(x+π/4)cos(2x+π/4) = cos(x+π/4 + 2x+π/4) + cos(x+π/4 - 2x - π/4)
= cos(3x+π/2) + cos(-x)
= cos(3x+π/2) + cos(x)

Now we have:
cos(3x+π/2) + cos(x) + sin3x

We can simplify the cosine term using the trigonometric identity that cos(3x+π/2) = -sin3x:
-sin3x + cos(x) + sin3x

The sin3x terms cancel out:
cos(x)

Therefore, the simplified expression is just cos(x).