5 cos x ctg x -5 ctg x +2 sin x = 0

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вопрос

To solve the equation 5cos(x)ctg(x) - 5ctg(x) + 2sin(x) = 0, we can first simplify and rewrite it in terms of sine and cosine functions.

Recall that ctg(x) is equivalent to 1/tan(x), so we can rewrite the equation as:

5cos(x)(1/tan(x)) - 5(1/tan(x)) + 2sin(x) = 0

Next, rewrite cosine and sine functions in terms of tangent:

cos(x) = 1/tan(x
sin(x) = tan(x)

Substitute these values into the equation:

5(1/tan(x))*(1/tan(x)) - 5(1/tan(x)) + 2tan(x) = 0

Simplify:

5/tan^2(x) - 5/tan(x) + 2tan(x) = 0

Multiply all terms by tan^2(x) to get rid of the denominator:

5 - 5tan(x) + 2tan^3(x) = 0

Rearrange the terms to get a cubic equation:

2tan^3(x) - 5tan(x) + 5 = 0

This is a cubic equation in terms of tan(x) and can be solved by methods such as factoring, using the cubic formula, or numerical methods.