Sqrt(3)-sqrt(6)*cosx=0

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вопрос

To solve the equation sqrt(3) - sqrt(6)*cos(x) = 0 for x, follow these steps:

Add sqrt(6)*cos(x) to both sides of the equation to isolate the square root term:

sqrt(3) = sqrt(6)*cos(x)

Square both sides of the equation to eliminate the square roots:

(√3)^2 = (√6cos(x))^
3 = 6cos(x)^2

Divide both sides of the equation by 6:

cos(x)^2 = 3/
cos(x)^2 = 1/2

Take the square root of both sides to solve for cos(x):

cos(x) = ±sqrt(1/2)

Since cos(x) can be either positive or negative in different quadrants, we need to consider both possibilities:

cos(x) = sqrt(1/2) (cosine of x in the first and fourth quadrants
cos(x) = -sqrt(1/2) (cosine of x in the second and third quadrants)

Solve for x using the inverse cosine function:

For cos(x) = sqrt(1/2)
x = π/4 + 2πn (x is in the first quadrant
x = 7π/4 + 2πn (x is in the fourth quadrant)

For cos(x) = -sqrt(1/2)
x = 3π/4 + 2πn (x is in the second quadrant
x = 5π/4 + 2πn (x is in the third quadrant)

Therefore, the solutions to the equation are
x = π/4 + 2πn, 3π/4 + 2πn, 5π/4 + 2πn, 7π/4 + 2π
where n is an integer.