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Find all solutions for 2cosx - root 3

User Kiranr
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Final answer:

The general solutions for the equation 2cos(x) - √3 = 0 are x = π/6 + 2nπ and x = 11π/6 + 2nπ for any integer n.

Step-by-step explanation:

To solve the mathematical problem completely, we need to find all solutions for the equation given by 2cos(x) - √3 = 0. Solving for cos(x), we have cos(x) = √3/2.

This value corresponds to an angle with a reference angle of π/6 in the unit circle, which gives us two solutions in the interval [0, 2π]: x = π/6 and x = 11π/6.

However, since the cosine function is periodic with a period of 2π, we can find a general solution for x by adding any integer multiple of 2π to these solutions.

Hence, the general solutions are x = π/6 + 2nπ and x = 11π/6 + 2nπ for any integer n.

User Rgchris
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