3sin^2 2x-2=sin2xcos2x

Предыдущий
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вопрос

To simplify the left side of the equation, we need to use the double angle identity for sine:

sin(2x) = 2sin(x)cos(x)

So, we can rewrite the left side of the equation as:

3(2sin(x)cos(x))^2 - 2 = sin(2x)cos(2x)

Expanding and simplifying further, we get:

12sin^2(x)cos^2(x) - 2 = sin(2x)cos(2x)

Now, we can use the double angle identity for cosine:

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

Substitute this into the equation:

12sin^2(x)cos^2(x) - 2 = sin(2x)(cos^2(x) - sin^2(x))

Expand and simplify:

12sin^2(x)cos^2(x) - 2 = sin(2x)cos^2(x) - sin(2x)sin^2(x)

Since sin(2x) = 2sin(x)cos(x), we have:

12sin^2(x)cos^2(x) - 2 = 2sin(x)cos(x)cos^2(x) - 2sin(x)cos(x)sin(x)

12sin^2(x)cos^2(x) - 2 = 2sin(x)cos^3(x) - 2sin^2(x)cos(x)

At this point, the equation cannot be simplified further without additional constraints or information.