Question

If tan(45) = 1 and tan (-45)= -1 , is tan(x) even or odd?

Answer 1

Answer:

A function is said to be 'odd' if:

$-f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x$

Therefore, $tan\:x$ is odd function.

Step-by-step explanation:

A function is said to be 'even' if:

$f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x$

A function is said to be 'odd' if:

$-f\left(x\right)\:=\:f\left(-x\right)\:for\:all\:x$

as

$tan\:\left(-45\right)\:=\:-1\:$

and we know that

                               $tan\:x=\frac{sin\:x}{cosx}$

                              $\:f\left(-x\right)=\frac{sin\left(-x\right)}{cos\left(-x\right)}=\frac{-sin\left(x\right)}{cos\left(x\right)}=-tan\left(x\right)=-f\left(x\right)$

Therefore, $tan\:x$ is odd function.

Answer 2

Answer:

Odd

Step-by-step explanation:

tan(-45) = -tan(45)