Question

Sin x + cos x =0 ребята срочно !!! Помогите

Answer 1

sinx + cosx = 0 |:cosx

tgx + 1 = 0

tgx = - 1

x = - pi/4 + pik, k ∈ Z

Answer 2

Solving the Equation sin(x) + cos(x) = 0

To solve the equation sin(x) + cos(x) = 0, we can use trigonometric identities and algebraic manipulation. Let's go through the steps:

1. Start with the equation sin(x) + cos(x) = 0. 2. Rearrange the equation by subtracting cos(x) from both sides: sin(x) = -cos(x). 3. Square both sides of the equation to eliminate the negative sign: sin^2(x) = cos^2(x). 4. Use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to substitute for cos^2(x): sin^2(x) = 1 - sin^2(x). 5. Simplify the equation: 2sin^2(x) = 1. 6. Divide both sides of the equation by 2: sin^2(x) = 1/2. 7. Take the square root of both sides of the equation: sin(x) = ±√(1/2).

Now, let's find the values of x that satisfy the equation.

The square root of 1/2 can be simplified as follows:

√(1/2) = ±√(1)/√(2) = ±1/√(2) = ±(1/√(2)) * (√(2)/√(2)) = ±(√(2)/2).

Therefore, we have two possible solutions for sin(x):

1. sin(x) = √(2)/2 2. sin(x) = -√(2)/2

To find the corresponding values of x, we can use the inverse sine function (also known as arcsin or sin^(-1)).

1. For sin(x) = √(2)/2: - x = arcsin(√(2)/2) = π/4 + 2πn, where n is an integer.

2. For sin(x) = -√(2)/2: - x = arcsin(-√(2)/2) = 3π/4 + 2πn, where n is an integer.

Therefore, the solutions to the equation sin(x) + cos(x) = 0 are:

- x = π/4 + 2πn, where n is an integer. - x = 3π/4 + 2πn, where n is an integer.

Please note that these solutions are not exhaustive, as there are infinitely many values of x that satisfy the equation. The solutions provided above represent the general form of the solutions.

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