To solve this trigonometric equation, we can apply the following trigonometric identities:
cos (π - x) = -cos(x)sin (π/2 + x) = cos(x)
So, the equation becomes:
-cos(x) - cos(x) = 1 -2cos(x) = 1 cos(x) = -1/2
Now, we need to find the value of x that satisfies this equation. Since cosine is negative in the second and third quadrants, we can determine that x is in the second or third quadrant where cosine is -1/2.
In the unit circle, cosine is -1/2 at π + π/3 and 2π - π/3.
Therefore, the solutions are x = π + π/3 or x = 2π - π/3.
To solve this trigonometric equation, we can apply the following trigonometric identities:
cos (π - x) = -cos(x)sin (π/2 + x) = cos(x)So, the equation becomes:
-cos(x) - cos(x) = 1
-2cos(x) = 1
cos(x) = -1/2
Now, we need to find the value of x that satisfies this equation. Since cosine is negative in the second and third quadrants, we can determine that x is in the second or third quadrant where cosine is -1/2.
In the unit circle, cosine is -1/2 at π + π/3 and 2π - π/3.
Therefore, the solutions are x = π + π/3 or x = 2π - π/3.