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:

Answer 3

To solve the trigonometric equation cos(x)cos(2x) = cos(3x), we'll use trigonometric identities and algebraic manipulations.

Step 1: Apply the double angle formula for cosine: cos(2x) = 2cos^2(x) - 1

Step 2: Substitute the value of cos(2x) in the equation: cos(x)(2cos^2(x) - 1) = cos(3x)

Step 3: Expand the equation: 2cos^3(x) - cos(x) = cos(3x)

Step 4: Use the triple angle formula for cosine: cos(3x) = 4cos^3(x) - 3cos(x)

Step 5: Substitute cos(3x) in the equation: 2cos^3(x) - cos(x) = 4cos^3(x) - 3cos(x)

Step 6: Rearrange the equation to one side: 2cos^3(x) - 4cos^3(x) + cos(x) - 3cos(x) = 0

Step 7: Combine like terms: -2cos^3(x) - 2cos(x) = 0

Step 8: Factor out -2cos(x): -2cos(x)(cos^2(x) + 1) = 0

Step 9: Set each factor to zero and solve for x:

1. -2cos(x) = 0 cos(x) = 0 x = π/2 + kπ, where k is an integer.

2. cos^2(x) + 1 = 0 This equation has no real solutions because the square of a real number is always greater than or equal to zero, and adding 1 cannot result in zero.

So, the solutions to the equation cos(x)cos(2x) = cos(3x) are x = π/2 + kπ, where k is an integer.