Question

3 cos^2 x - 2 sin x = 3 - 3 sin^2 x

Answer 1

3 cos^2 x - 2 sin x = 3 - 3 sin^2 x
3 cos^2 x + 3 sin^2 x - 2 sin x = 3
3 (cos^2 x +  sin^2 x) - 2 sin x = 3
3*1 - 2sin x = 3
2sin x= 3-3 = 0
sin x = 0
x = Arc sin 0 = kπ.

Answer 2

We can start by simplifying the right-hand side of the equation using the identity:

sin^2(x) + cos^2(x) = 1

Rearranging this equation, we get:

sin^2(x) = 1 - cos^2(x)

Substituting this into the right-hand side of the equation, we get:

3 - 3 sin^2(x) = 3 - 3(1 - cos^2(x)) = 3cos^2(x)

So the equation simplifies to:

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

Subtracting 3cos^2(x) from both sides, we get:

-2sin(x) = 0

Dividing by -2, we get:

sin(x) = 0

Therefore, the solutions to the equation are values of x for which sin(x) = 0. These are the multiples of pi, i.e., x = n*pi where n is an integer.