Question

4sin 2 x cos 2x => 1

Answer 1

Объяснение:

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Answer 2

To simplify the expression 4sin(2x)cos(2x), you can use the double-angle identities for sine and cosine. The double-angle identities are:

1. sin(2θ) = 2sin(θ)cos(θ)
2. cos(2θ) = cos²(θ) - sin²(θ)

Let's simplify the given expression step by step:

4sin(2x)cos(2x)

Using the double-angle identity for sine (1):

= 4 * (2sin(x)cos(x)) * cos(2x)

Now, let's use the double-angle identity for cosine (2):

= 4 * (2sin(x)cos(x)) * (cos²(x) - sin²(x))

We can further simplify the expression:

= 4 * (2sin(x)cos(x)) * (1 - sin²(x))

Next, we can apply the identity sin²(x) = 1 - cos²(x):

= 4 * (2sin(x)cos(x)) * (1 - cos²(x))

Now, we have an expression in terms of cos(x) and sin(x) only. If there was an additional equation or constraint given in the problem, we could proceed to find a specific value for the expression. Without additional information or an equation set to solve, we cannot simplify the expression further to a single numeric value.

If you have additional information or constraints, please provide them, and I'll be happy to help you further.