Which of the following is an odd function?

Given:

To find:

The odd function.

Solution:

If f(-x) = -f(x), then the function is odd.

If f(-x) = f(x), then the function is even.

Option A:

Substitute x = -x

          ≠ - f(x)

It is not odd function.

Option B:

Substitute x = -x

            (Since )

          ≠ - f(x)

It is not odd function.

Option C:

Substitute x = -x

          ≠ - f(x)

It is not odd function.

Option D:

Substitute x = -x

It is odd function.

Therefore, f(x) = -x is an odd function.

cotΘ = -

Step-by-step explanation:

Using the trigonometric identities

cot x =

sin²x + cos²x = 1 ⇒ cosx = ±

Since Θ is in second quadrant then cosΘ < 0

cosΘ = - )^2

        = - = - = -

Hence

cotΘ =

        = - ×

        = - = -