Решение тригонометрических уравнений cos2x-cosx=0

cos2x - cosx = 0

Distribute the cos2x term: cos^2(x) - cosx = 0

Use the identity cos^2(x) = 1 - sin^2(x): 1 - sin^2(x) - cosx = 0

Rearrange the terms: sin^2(x) + cosx - 1 = 0

Since sin^2(x) + cos^2(x) = 1, we can rewrite sin^2(x) as 1 - cos^2(x): 1 - cos^2(x) + cosx - 1 = 0

Simplify: -cos^2(x) + cosx = 0

Factor out a negative sign: cosx(cosx - 1) = 0

Set each factor to zero: cosx = 0 or cosx - 1 = 0

Solve for x: Case 1: cosx = 0 x = π/2 + πn, где n - целое число

Case 2: cosx - 1 = 0 cosx = 1 x = 2πn, где n - целое число

Ответ: x = π/2 + πn, x = 2πn