Which of the following is NOT a solution to cos^2x=3sin^2x?
A.) 30 degrees
B.) 60 degrees
C.) 150 degrees
D.)210 degrees
E.)330 degrees
well, you have
tan^2 x = 1/3
which angle does not have tan x = ±1/√3 ?
To determine which of the given angles is NOT a solution to the equation cos^2x = 3sin^2x, we can substitute the angles into the equation and check if the equation holds true.
First, let's rewrite the equation using the trigonometric identity: cos^2x = 1 - sin^2x.
So, the equation becomes: 1 - sin^2x = 3sin^2x.
Combine the like terms: 4sin^2x = 1.
Divide both sides by 4: sin^2x = 1/4.
Now, take the square root of both sides: sinx = ± √(1/4).
The positive square root gives us sinx = 1/2, while the negative square root gives us sinx = -1/2.
Now, we can use the inverse sine function to find the values of x for which sinx = 1/2 or sinx = -1/2.
For sinx = 1/2:
x = arcsin(1/2) = 30 degrees
For sinx = -1/2:
x = arcsin(-1/2) = -30 degrees (not listed in the options)
From the given options:
A.) 30 degrees -> It is a solution to the equation.
B.) 60 degrees -> It is a solution to the equation.
C.) 150 degrees -> It is a solution to the equation.
D.) 210 degrees -> It is a solution to the equation.
E.) 330 degrees -> It is a solution to the equation.
Therefore, the angle that is NOT a solution to the equation is -30 degrees, which is not listed among the given options.