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Is cos(x3 - x + 2) even or odd?
Trigonometry is the branch of maths that deals with the relationships between sides and angles of a right angles triangle.
Answer: cos (x3 - x + 2) is neither even nor odd.
Let's understand the solution.
To check for an odd function f(x), we need to verify if f(-x) = -f(x), and to check for even functions we check if it follows the relation f(-x) = f(x).
⇒ f(x) = cos (x3 - x + 2)
Since cos x is positive on the first and the fourth quadrant and -x is the angle taken from the x-axis in a clockwise direction, hence lying in the fourth quadrant. We have cos (-x) = cos x.
⇒ f(-x) = cos ((-x)3 - (-x) + 2)
⇒ f(-x) = cos (-x3 + x + 2) ≠ cos (x3 - x + 2)
⇒ - f(x) = - cos (x3 - x - 2) ≠ cos (x3 - x + 2)
⇒ f(-x) ≠ - f(x) and f(-x) ≠ f(x)
Hence, it neither follows conditions for odd functions nor follows for even functions.
Therefore, Cos (x3 - x + 2) is neither even nor odd.