Answer:
[tex]tan(-\theta)=-tan\theta[/tex]
Odd function
Step-by-step explanation:
We are given that
[tex]tan(-\theta)[/tex]
We have to determine the value of [tex]tan(-\theta)[/tex]and find tangent function is odd,even or neither.
[tex]tan(-\theta)=\frac{sin(-\theta)}{cos(-\theta)}[/tex]
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]
We know that
[tex]sin(-\theta)=-sin\theta[/tex]
[tex]cos(-\theta)=cos\theta[/tex]
By using identities
Then, we get
[tex]tan(-\theta)=\frac{-sin\theta}{cos\theta}=-tan\theta[/tex]
[tex]tan(-\theta)=-tan\theta[/tex]
Odd function: If [tex]f(-x)=-f(x)[/tex]
Even function:If [tex]f(-x)=f(x)[/tex]
[tex]tan(-\theta)=-tan\theta[/tex]
Therefore, function is an odd function.
