Trigonometry Identities Table

${\displaystyle \sin ^{2}+\cos ^{2}=1}$	${\displaystyle 1+\tan ^{2}=\sec ^{2}}$
${\displaystyle \sin({\frac {\pi }{2}}-\theta )=\cos \theta }$	${\displaystyle \cos({\frac {\pi }{2}}-\theta )=\sin \theta }$
${\displaystyle \sec({\frac {\pi }{2}}-\theta )=\csc \theta }$	${\displaystyle \csc({\frac {\pi }{2}}-\theta )=\sec \theta }$
${\displaystyle \sin(-\theta )=-\sin \theta }$	${\displaystyle \cos(-\theta )=\cos \theta }$
${\displaystyle \sin 2\theta =2\sin \theta \cos \theta }$	${\displaystyle \cos 2\theta =\cos ^{2}-\sin ^{2}=2\cos ^{2}\theta -1=1-2\sin ^{2}\theta }$
${\displaystyle \sin ^{2}\theta ={\frac {1-\cos 2\theta }{2}}}$	${\displaystyle \cos ^{2}\theta ={\frac {1+\cos 2\theta }{2}}}$
${\displaystyle \sin \alpha +\sin \beta =2\sin({\frac {\alpha +\beta }{2}})\cos({\frac {\alpha -\beta }{2}})}$	${\displaystyle \sin \alpha -\sin \beta =2\cos({\frac {\alpha +\beta }{2}})\sin({\frac {\alpha -\beta }{2}})}$
${\displaystyle \cos \alpha +\cos \beta =2\cos({\frac {\alpha +\beta }{2}})\cos({\frac {\alpha -\beta }{2}})}$	${\displaystyle \cos \alpha -\cos \beta =-2\sin({\frac {\alpha +\beta }{2}})\sin({\frac {\alpha -\beta }{2}})}$
${\displaystyle \sin \alpha \sin \beta ={\frac {1}{2}}[\cos(\alpha -\beta )-\cos(\alpha +\beta )]}$	${\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}[\cos(\alpha -\beta )+\cos(\alpha +\beta )]}$
${\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}[\sin(\alpha +\beta )+\sin(\alpha -\beta )]}$	${\displaystyle 1+\cot ^{2}=\csc ^{2}}$
${\displaystyle e^{j\theta }=\cos \theta +j\sin \theta }$	${\displaystyle \cos \theta ={\frac {e^{j\theta }+e^{-j\theta }}{2}}}$
${\displaystyle \tan({\frac {\pi }{2}}-\theta )=\cot \theta }$	${\displaystyle \cot({\frac {\pi }{2}}-\theta )=\tan \theta }$
${\displaystyle \tan(-\theta )=-\tan \theta }$	${\displaystyle \tan 2\theta ={\frac {2\tan \theta }{1-tan^{2}\theta }}}$
${\displaystyle \tan ^{2}\theta ={\frac {1-\cos 2\theta }{1+\cos 2\theta }}}$	${\displaystyle \sin \theta ={\frac {e^{j\theta }-e^{-j\theta }}{j2}}}$

References

1. Trigonometric Identities