To solve the equation 2sinx - cos^2(x)sinx = 0, we can factor out a sinx term:
sinx(2 - cos^2(x)) = 0
Now, we have two possibilities for sinx to be equal to 0 or for (2 - cos^2(x)) to be equal to 0:
1) sinx = 0: This implies x = nπ, where n is an integer.
2) 2 - cos^2(x) = 0: cos^2(x) = 2 cos(x) = ±√2
The solutions for cos(x) = ±√2 are not in the range of values for the cosine function (-1 <= cos(x) <= 1). Therefore, there are no solutions for this part of the equation.
In conclusion, the solution to the equation 2sinx - cos^2(x)sinx = 0 is x = nπ, where n is an integer.
To solve the equation 2sinx - cos^2(x)sinx = 0, we can factor out a sinx term:
sinx(2 - cos^2(x)) = 0
Now, we have two possibilities for sinx to be equal to 0 or for (2 - cos^2(x)) to be equal to 0:
1) sinx = 0:
This implies x = nπ, where n is an integer.
2) 2 - cos^2(x) = 0:
cos^2(x) = 2
cos(x) = ±√2
The solutions for cos(x) = ±√2 are not in the range of values for the cosine function (-1 <= cos(x) <= 1). Therefore, there are no solutions for this part of the equation.
In conclusion, the solution to the equation 2sinx - cos^2(x)sinx = 0 is x = nπ, where n is an integer.