Solve the equation 2cos^2x + 3sinx = 3

x = 2 π n_1 + π/2 for n_1 element Z

or x = 2 π n_2 + (5 π)/6 for n_2 element Z or x = 2 π n_3 + π/6 for n_3 element Z

Step-by-step explanation:

Solve for x:

2 cos^2(x) + 3 sin(x) = 3

Write 2 cos^2(x) + 3 sin(x) = 3 in terms of sin(x) using the identity cos^2(x) = 1 - sin^2(x):

-1 + 3 sin(x) - 2 sin^2(x) = 0

The left hand side factors into a product with three terms:

-(sin(x) - 1) (2 sin(x) - 1) = 0

Multiply both sides by -1:

(sin(x) - 1) (2 sin(x) - 1) = 0

Split into two equations:

sin(x) - 1 = 0 or 2 sin(x) - 1 = 0

Add 1 to both sides:

sin(x) = 1 or 2 sin(x) - 1 = 0

Take the inverse sine of both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) - 1 = 0

Add 1 to both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) = 1

Divide both sides by 2:

x = 2 π n_1 + π/2 for n_1 element Z

or sin(x) = 1/2

Take the inverse sine of both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or x = 2 π n_2 + (5 π)/6 for n_2 element Z or x = 2 π n_3 + π/6 for n_3 element Z

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

are you an artist's daughter? cuz dang you a fine piece of art, girl.