Question

Решить уравнение (2sinx-1)(√cosx+1)=0

Answer 1

если под корнем все выражение (cosx+1),то решение на фото.

если под корнем только cosx,то один корень один,так как,√cosx не может равняться -1

Answer 2

To solve the equation (2sinx - 1)(√cosx + 1) = 0, we need to find the values of x that make the left-hand side equal to zero. This means that either (2sinx - 1) = 0 or (√cosx + 1) = 0.

1. Solving (2sinx - 1) = 0: Add 1 to both sides: 2sinx = 1

Now, divide both sides by 2: sinx = 1/2

The solutions to this part of the equation can be found using the unit circle or trigonometric identities. The solutions for sinx = 1/2 are:

x = π/6 + 2πn or x = 5π/6 + 2πn

where n is an integer (n = 0, ±1, ±2, ...).

2. Solving (√cosx + 1) = 0: Subtract 1 from both sides: √cosx = -1

Since cosine values are never less than -1, there are no real solutions to this part of the equation.

Combining both solutions, we have:

x = π/6 + 2πn or x = 5π/6 + 2πn

where n is an integer (n = 0, ±1, ±2, ...).