Question

Solve cos x + rad 2 = -cos x for over the interval [0, 2pi ]

Answer 1

Option C is the answer

Explanation:

Answer 2

`cos x + √(2) = -cosx \\ \\ 2 cos x + √(2) = 0 \\ \\ cos x = -(√(2))/(2)`

The cosine function is negative in 2nd and 3rd quadrants, So you know that you will have 2 solutions. One between pi/2 and pi, the other between pi and 3pi/2.

Refer to a unit circle to find that

`cos ((3\pi)/(4)) = -(√(2))/(2) \\ \\ cos ((5\pi)/(4)) = -(√(2))/(2)`

Final Answer:

`x = (3\pi)/(4), (5\pi)/(4)`