Question

1+2sinxcos2x=0 / / / /

Answer 1

Ответ:

sinx=0 или cos2x=0

x=πn, n∈z; 2x=π/2+πk,k∈z

                     x=π/4+πk/2, k∈z

Объяснение:

Answer 2

To solve the equation 1 + 2sin(x)cos(2x) = 0, we can follow these steps:

Step 1: Rewrite cos(2x) using a trigonometric identity. Step 2: Substitute the value of cos(2x) into the equation. Step 3: Solve the resulting equation for sin(x). Step 4: Solve for x.

Let's go through these steps in detail:

Step 1: Rewrite cos(2x) using a trigonometric identity. We know the identity: cos(2x) = 1 - 2sin^2(x). Let's use this identity.

Step 2: Substitute the value of cos(2x) into the equation. Replace cos(2x) with 1 - 2sin^2(x) in the original equation: 1 + 2sin(x)(1 - 2sin^2(x)) = 0

Step 3: Solve the resulting equation for sin(x). Distribute the sin(x) term: 1 + 2sin(x) - 4sin^3(x) = 0

Step 4: Solve for x. Now we have a cubic equation in terms of sin(x): -4sin^3(x) + 2sin(x) + 1 = 0

This is a cubic equation that may not have a simple analytical solution. You might need to use numerical methods to approximate the solutions. You can use methods like the Newton-Raphson method or a numerical solver to find the values of sin(x) that satisfy the equation.

Keep in mind that this process might result in multiple solutions for sin(x), and from there, you can find corresponding values of x using the inverse sine function (arcsin).

Please note that due to the complexity of the equation, the solutions may not be straightforward and may require numerical techniques or software tools to find accurate solutions.