Answer:
A function is said to be 'odd' if:
[tex]-f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x[/tex]
Therefore, [tex]tan\:x[/tex] is odd function.
Step-by-step explanation:
A function is said to be 'even' if:
[tex]f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x[/tex]
A function is said to be 'odd' if:
[tex]-f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x[/tex]
as
[tex]tan\:\left(-45\right)\:=\:-1\:[/tex]
and we know that
[tex]tan\:x=\frac{sin\:x}{cosx}[/tex]
[tex]\:f\left(-x\right)=\frac{sin\left(-x\right)}{cos\left(-x\right)}=\frac{-sin\left(x\right)}{cos\left(x\right)}=-tan\left(x\right)=-f\left(x\right)[/tex]
Therefore, [tex]tan\:x[/tex] is odd function.
