این نوشتار شامل فهرستی از فهرست اتحادهای مثلثاتی است.

${\displaystyle 1+\tan ^{2}\theta =\sec ^{2}\theta }$

${\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }$

${\displaystyle \cos(\theta +\beta )=\cos \theta .\cos \beta -\sin \theta .\sin \beta \,}$

${\displaystyle \cos(\theta -\beta )=\cos \theta .\cos \beta +\sin \theta .\sin \beta \,}$

${\displaystyle \sin(\theta +\beta )=\sin \theta .\cos \beta +\cos \theta .\sin \beta \,}$

${\displaystyle \sin(\theta -\beta )=\sin \theta .\cos \beta -\cos \theta .\sin \beta \,}$

${\displaystyle \tan(\theta +\beta )={\frac {\tan \theta +\tan \beta }{1-\tan \theta .\tan \beta }}\,}$

${\displaystyle \tan(\theta -\beta )={\frac {\tan \theta -\tan \beta }{1+\tan \theta .\tan \beta }}\,}$

${\displaystyle \cot(\theta +\beta )={\frac {\cot \theta .\cot \beta -1}{\cot \theta +\cot \beta }}\,}$

${\displaystyle \cot(\theta -\beta )={\frac {\cot \theta .\cot \beta +1}{\cot \beta -\cot \theta }}\,}$

${\displaystyle \sin(2\theta )=2\sin \theta \cos \theta ={\frac {2\tan \theta }{1+\tan ^{2}\theta }}}$

${\displaystyle \cos(2\theta )=\cos ^{2}\theta -\sin ^{2}\theta =2\cos ^{2}\theta -1=1-2\sin ^{2}\theta ={\frac {1-\tan ^{2}\theta }{1+\tan ^{2}\theta }}}$

${\displaystyle \tan(2\theta )={\frac {2\tan \theta }{1-\tan ^{2}\theta }}}$

${\displaystyle \cot(2\theta )={\frac {\cot ^{2}\theta -1}{2\cot \theta }}}$

${\displaystyle \sec(2\theta )={\frac {\sec ^{2}\theta }{2-\sec ^{2}\theta }}}$

${\displaystyle \csc(2\theta )={\frac {\sec \theta \csc \theta }{2}}}$

${\displaystyle \sin 3\theta =3\sin \theta -4\sin ^{3}\theta }$

${\displaystyle \cos 3\theta =4\cos ^{3}\theta -3\cos \theta }$

${\displaystyle \tan 3\theta ={\frac {3\tan \theta -\tan ^{3}\theta }{1-3\tan ^{2}\theta }}}$

${\displaystyle \cos ^{2}\phi ={\frac {1}{2}}\ (1+\cos 2\phi )}$

${\displaystyle \sin ^{2}\phi ={\frac {1}{2}}\ (1-\cos 2\phi )}$

${\displaystyle \tan {\frac {\phi }{2}}\ ={\frac {\sin \phi }{1+\cos \phi }}\ }$

${\displaystyle \sin a.\cos b={\frac {\sin(a+b)+\sin(a-b)}{2}}}$

${\displaystyle \cos a.\cos b={\frac {\cos(a+b)+\cos(a-b)}{2}}}$

${\displaystyle \sin a.\sin b={\frac {\cos(a-b)-\cos(a+b)}{2}}}$

${\displaystyle \sin a\pm \sin b=2\sin({\frac {a\pm b}{2}}).\cos({\frac {a\mp b}{2}}\,)}$

${\displaystyle \cos a+\cos b=2\cos({\frac {a+b}{2}}).\cos({\frac {a-b}{2}}\,)}$

${\displaystyle \cos a-\cos b=-2\sin({\frac {a+b}{2}}).\sin({\frac {a-b}{2}}\,)}$

${\displaystyle \tan a\pm \ tanb={\frac {\sin(a\pm b)}{\cos a\cos b}}}$

${\displaystyle \displaystyle \sin \theta \pm \cos \theta ={\sqrt {2}}sin(\theta \pm {\frac {\pi }{4}})}$

${\displaystyle {\frac {1\pm \tan x}{1\mp \tan x}}=\tan(\pi /4\pm x)}$

${\displaystyle \tan(\pi /2-x)=\cot(x)}$

آرتور کاکسفورد. اصول و کاربردهای مثلثات. ترجمهٔ عادل ارشقی. انتشارات رسا.

بهمن اصلاح پذیر. حسابان. شرکت چاپ و نشر کتاب‌های درسی ایران.

احمد فیروزنیا. مثلثات. سازمان پژوهش و برنامه‌ریزی آموزشی.