Question

1+2 sin ^2 x = sin 2 x У меня получился дискриминант меньше 0 , нет корней...

Answer 1

$1+2sin^{2}x=sin2x cos^{2}x+sin^{2}x+2sin^{2}x-sin2x=0 cos^{2}x+sin^{2}x+2sin^{2}x-2sinx*cosx=0 cos^{2}x+3sin^{2}x-2sinx*cosx=0/:cos^{2}x 3tg^{2}x-2tgx+1=0 D=(-2)^{2}-4*3*1=4-12=-8$

Answer 2

Solving the Equation 1 + 2sin^2(x) = sin(2x)

To solve the equation 1 + 2sin^2(x) = sin(2x) and determine the nature of its roots, we can follow these steps:

1. Equation Analysis: - The given equation is 1 + 2sin^2(x) = sin(2x). - We need to solve for the values of x that satisfy this equation and determine the nature of the roots.

2. Applying Trigonometric Identities: - We can use trigonometric identities to simplify the equation and solve for x.

3. Using Trigonometric Identities to Simplify: - By using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the equation as 1 + 2sin^2(x) = 2sin(x)cos(x).

4. Solving for x: - We can then proceed to solve for the values of x that satisfy this equation and determine the nature of the roots.

Conclusion

After analyzing the equation 1 + 2sin^2(x) = sin(2x) and applying trigonometric identities, we can solve for the values of x that satisfy the equation and determine the nature of the roots.