Cos7x cos2x+sin7x sin2x=1/3

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вопрос

To simplify this trigonometric expression, we can use the angle addition formula for cosine:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Using this formula, we can rewrite the expression as:

cos(7x + 2x) = 1/3
cos(9x) = 1/3

Now, we need to find the value of x that satisfies this equation. Since the cosine function has a period of 2π, we can find one solution in the interval [0, 2π) and then add multiples of 2π to find other solutions.

In the interval [0, 2π), the value of x that satisfies cos(9x) = 1/3 is approximately x = 0.439822

Therefore, the solution to the trigonometric expression is x ≈ 0.439822 + 2πn, where n is an integer.