Cosxcos2x=cos3x пжжжжжжжж

Question

Cosxcos2x=cos3x пжжжжжжжж

Answer 1

Ответ:

cos x cos 2x = cos x cos 2x − sin x sin 2x,

sin x sin 2x = 0.

Ответ: x = ½πn, n ∈ ℤ.

Пошаговое объяснение:

По формуле cos (α + β) = cos α cos β − sin α sin β получаем:

cos 3x = cos (x + 2x) = cos x cos 2x − sin x sin 2x.

Answer 2

Оhttps://tex.z-dn.net/?f=cosxcos2x%3Dcos3x%0A%5C%5C%5C%0A%20%5Cfrac%7B1%7D%7B2%7D%20%28cos%28x%2B2x%29%2Bcos%28x-2x%29%3Dcos3x%0A%5C%5C%5C%0Acos3x%2Bcosx%3D2cos3x%0Acos3x-cosx%3D0%0A%5C%5C%5C%0A-2sin%20%5Cfrac%7B3x%2Bx%7D%7B2%7Dsin%20%5Cfrac%7B3x-x%7D%7B2%7D%3D0%0A%5C%5C%5C%0Asin2xsinx%3D0%0A%5C%5C%5C%0Asinx%3D0%0A%5C%5C%5C%0Ax%3D%5Cpi%20n%2C%20n%5Cin%20Z%0A%5C%5C%5C%0Asin2x%3D0%0A%5C%5C%5C%0A2x%3D%5Cpi%20n%0A%5C%5C%5C%0Ax%3D%20%5Cfrac%7B%5Cpi%20n%7D%7B2%7D%20%2C%20n%5Cin%207

ответ 5 корней

Пошаговое объяснение: