Question

How do I solve this:
2(cos^2 x - 1) = -1

Answer 1

\[x=(\frac{ \pi n }{ 2 }-\frac{ \pi }{ 4 } ) , n \in z\]

Answer 2

Can you please explain how you solved this? I have a test tommorow and need to be able to repeat these procedures.

Answer 3

Anyone?

Answer 4

Solve for x:
2 (cos^2(x)-1) = -1
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
cos^2(x)-1 = -1/2
Isolate terms with x to the left hand side.
Add 1 to both sides:
cos^2(x) = 1/2
Eliminate the exponent on the left hand side.
Take the square root of both sides:
cos(x) = 1/sqrt(2) or cos(x) = -1/sqrt(2)
Look at the first equation: Eliminate the cosine from the left hand side.
Take the inverse cosine of both sides:
x = pi/4+2 pi n_1 for n_1 element Z or x = (7 pi)/4+2 pi n_2 for n_2 element Z
or cos(x) = -1/sqrt(2)
Look at the third equation: Eliminate the cosine from the left hand side.
Take the inverse cosine of both sides:
Answer: |
| x = pi/4+2 pi n_1 for n_1 element Z
or x = (7 pi)/4+2 pi n_2 for n_2 element Z
or x = (3 pi)/4+2 pi n_3 for n_3 element Z or x = (5 pi)/4+2 pi n_4 for n_4 element Z