# Find in degrees the solution x of the equation 1-2cos2x = 0, satisfying the conditions 0.

August 29, 2021 | education

| Multiplying the equation by -1, we get:

-1 + 2cos (2x) = 0;

cos (2x) = 1/2.

The roots of an equation of the form cos (x) = a are determined by the formula: x = arccos (a) + – 2 * π * n, where n is a natural number. We get:

2x = arccos (1/2) + – 2 * π * n.

2x = π / 3 + – 2 * π * n;

x = π / 6 + – π * n.

Find the roots belonging to a given interval:

0 <= π / 6 + – π * n <= π / 3.

-1/6 <+ – n <1/6.

n = 0.

Then x = π / 6.

Answer: x belongs to {π / 6}.

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