11/12 sin 2 12y+11/12 cos 2 12y

Предыдущий
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вопрос

To simplify the expression, we can first rewrite sin(2x) and cos(2x) using the double angle identities:

sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x)

Plugging these into the expression gives:

(11/12)2sin(12y)cos(12y) + (11/12)(cos^2(12y) - sin^2(12y))

Now we simplify each term separately:

2sin(12y)cos(12y) = sin(24y) = (1/2)sin(24y)

cos^2(12y) - sin^2(12y) = cos(24y)

Putting these together, we get:

(1/2)*(11/12)sin(24y) + (11/12)cos(24y)

Multiplying through by (11/12), we get:

(11/24)sin(24y) + (11/12)cos(24y)

Therefore, the simplified expression is (11/24)sin(24y) + (11/12)cos(24y).