Question

Cos2x-0.25=cos^2x помогите пожалуйста

Answer 1

cos2x-0.25=cos²x

cos²х - sin²x - 0.25 = cos²x

sin²x = - 0.25

1) sinx = - 0.5

x₁ = (-1)^(k + 1) · π/6 + πk

2) sinx = 0.5

x₂ = (-1)^k · π/6 + πk

 

Answer 2

cos 2x= cos^2x-sin^2x

cos^2x-sin^2x-cos^2x=0.25

sin^2x=-1/4

sin x=1/2

sin x=-1/2

Answer 3

Solving the Equation Cos2x - 0.25 = cos^2x

To solve the equation cos2x - 0.25 = cos^2x, we can use trigonometric identities and algebraic manipulation.

First, let's rewrite the equation using the double angle identity for cosine: cos2x = 2cos^2x - 1

Now, substitute cos2x in the original equation: 2cos^2x - 1 - 0.25 = cos^2x

Combine like terms: 2cos^2x - 1.25 = cos^2x

Subtract cos^2x from both sides: cos^2x = 1.25

Take the square root of both sides: cosx = ±√1.25

Finally, solve for x by taking the inverse cosine of both sides: x = ±arccos(√1.25)

The solutions for x will depend on the range of the inverse cosine function, typically between 0 and 180 degrees or 0 and π radians.

This process provides a general approach to solving the given equation cos2x - 0.25 = cos^2x.