Even and Odd Identities

Derived from the periodic nature of cos, sin and tan functions

Derivation

Cosine

the cosine function is an even function. f(x) = f(-x) Thus, $\cos (x)=\cos (-x)$

Sine

the sine function is an odd function. f(-x) = -f(x) Thus, $\sin (-x)=-\sin (x)$

Tangent

Believe it or not, tangent function is also an odd function f(-x) = -f(x) $\tan (-x)=-\tan (x)$

Identities

$\cos (x)=\cos (-x)$

$\sin (-x)=-\sin (x)$

$\tan (-x)=-\tan (x)$