Question

Чему равен cos(x-3П/2)? И как решить уравнение: cos^2(x-3П/2)=1+cos^2x. Помогите пожалуйста с уравнением!!! оно из кдр за январь 2008 года 10 класса

Answer 1

cos(x - 3π/2) = cos(-(3π/2 - x)) = cos(3π/2 - x) = -sin x;

cos^2 (x - 3π/2) = 1 + cos^2 x,

(-sin x)^2 = 1 + cos^2 x,

sin^2 x  -  cos^2 x = 1,

cos^2 x - sin^2 x = -1,

cos 2x = -1,

2x = π + 2πk, k∈Z,

x = π/2 + πk, k∈Z.

 

Answer 2

Cosine Function and Equation Solving

The value of cos(x-3π/2) can be determined using the trigonometric identity:

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Substituting a = x and b = 3π/2, we get:

cos(x-3π/2) = cos(x)cos(3π/2) + sin(x)sin(3π/2)

Using the values of cos(3π/2) and sin(3π/2), we can calculate the result.

To solve the equation cos^2(x-3π/2) = 1 + cos^2(x), we can use trigonometric identities to simplify and solve for x. Let's break it down step by step.

Solving the Equation

First, we can use the identity cos^2(x) + sin^2(x) = 1 to simplify the equation:

cos^2(x-3π/2) = 1 + cos^2(x)

Using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we can express cos^2(x-3π/2) in terms of cos(x) and sin(x).

Applying Trigonometric Identities

We have: cos^2(x-3π/2) = cos^2(x)cos^2(3π/2) + sin^2(x)sin^2(3π/2)

Substituting the values of cos(3π/2) and sin(3π/2), we can simplify the equation further.

Solving for x

After simplifying, we can solve for x by using algebraic manipulations and trigonometric identities. The goal is to isolate x on one side of the equation.

Once we have the simplified equation, we can proceed with solving for x by applying appropriate trigonometric identities and algebraic techniques.

Let's work through the steps to solve the equation and find the value of x.