Question

cosx - 2sinx = 0 Решите пожалуйста

Answer 1

поделить на cosx

получим 1-tgx=0

2tgx=1

tgx=0.5

x=arctg0.5

Answer 2

Problem Statement

We are given the equation cos(x) - 2sin(x) = 0 and we need to solve for x.

Solution

To solve the equation cos(x) - 2sin(x) = 0, we can use trigonometric identities and algebraic manipulations.

Let's rewrite the equation as cos(x) = 2sin(x).

We know that sin^2(x) + cos^2(x) = 1 (trigonometric identity).

Squaring both sides of the equation cos(x) = 2sin(x), we get:

(cos(x))^2 = (2sin(x))^2

Expanding and simplifying, we have:

cos^2(x) = 4sin^2(x)

Using the trigonometric identity sin^2(x) = 1 - cos^2(x), we can substitute this into the equation:

cos^2(x) = 4(1 - cos^2(x))

Expanding and simplifying further, we get:

cos^2(x) = 4 - 4cos^2(x)

Rearranging the terms, we have:

5cos^2(x) = 4

Dividing both sides by 5, we get:

cos^2(x) = 4/5

Taking the square root of both sides, we have:

cos(x) = ±√(4/5)

Now, let's solve for x.

Taking the inverse cosine (cos^(-1)) of both sides, we get:

x = cos^(-1)(±√(4/5))

The solutions for x are given by:

x = cos^(-1)(√(4/5)) and x = cos^(-1)(-√(4/5))

To find the values of x, we can use a calculator or a trigonometric table.

Let's summarize the solutions:

x = cos^(-1)(√(4/5)) and x = cos^(-1)(-√(4/5))

Please note that the solutions are given in radians.

I hope this helps! Let me know if you have any further questions.