6sinx*cosx-4cosx+sinx-2=0

Предыдущий
вопрос Следующий
вопрос

To solve the equation 6sinx*cosx - 4cosx + sinx - 2 = 0, we can first collect like terms:

sinx(6cosx + 1) - 4cosx - 2 = 0

Now, we notice that we have a common factor of cosx between the first two terms, so we can factor it out:

cosx(6sinx + 1) - 2(2cosx + 1) = 0

Now, we can factor out the common factor of (2cosx + 1) from the remaining terms:

(2cosx + 1)(3sinx - 2) = 0

Now, we set each factor equal to zero to find the solutions:

2cosx + 1 = 0
cosx = -1/2
x = 2π/3, 4π/3 (since cosine is negative in the second and third quadrants)

3sinx - 2 = 0
3sinx = 2
sinx = 2/3
x = π/3, 5π/3

Therefore, the solutions to the equation 6sinx*cosx - 4cosx + sinx - 2 = 0 are x = 2π/3, 4π/3, π/3, and 5π/3.