لە ئینسایکڵۆپیدیای ئازادی ویکیپیدیاوە
ھاوئەنجامە سێگۆشەییەکان(بە ئینگلیزی: Trigonometric identities) ئەو ھاوکێشانەن کە ھەر چەندە گۆڕانکاری لە بەھایەکانی گۆڕەکەکانیاندا بکرێت، بە ڕاستی دەمێنێتەوە.
هاوئەنجامی پیتاگۆرسییەکان[دەستکاری]
ھاوئەنجامە سێگۆشەییە بنەڕەتییەکان:
![{\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9333418071b0b0662ba53f8983fe1cbb613ad005)
![{\displaystyle 1+\tan ^{2}\theta =\sec ^{2}\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e65a44a4f54eea9ec39f392cb406af0be301e0)
![{\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/569181e0b7d46ae94b93ef730ec2f4374dca2ced)
ھاوئەنجامەکانی سەرجەم و جیاوازی:
![{\displaystyle \cos(\theta +\beta )=\cos \theta .\cos \beta -\sin \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73815b05a97c6c08b1fe4adefe492b356d09c254)
![{\displaystyle \cos(\theta -\beta )=\cos \theta .\cos \beta +\sin \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/721f66568f55ddbadeb07c1a331a92abbe26eb82)
ھاوئەنجامەکانی سەرجەم و جیاوازی:
![{\displaystyle \sin(\theta +\beta )=\sin \theta .\cos \beta +\cos \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61d3f85ddb9898794ae527714c7502b7023b0965)
![{\displaystyle \sin(\theta -\beta )=\sin \theta .\cos \beta -\cos \theta .\sin \beta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f415226aa28dff571ce7f028423f486105c43064)
![{\displaystyle \tan(\theta +\beta )={\frac {\tan \theta +\tan \beta }{1-\tan \theta .\tan \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0dd3bd706b3facee6720a8625c772b8df2f4a442)
![{\displaystyle \tan(\theta -\beta )={\frac {\tan \theta -\tan \beta }{1+\tan \theta .\tan \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0f729bed70209d97446e169ae665713ca096fbe)
![{\displaystyle \cot(\theta +\beta )={\frac {\cot \theta .\cot \beta -1}{\cot \theta +\cot \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1fbe8b6fc5145acdfbfc66eba0766a99396406c8)
![{\displaystyle \cot(\theta -\beta )={\frac {\cot \theta .\cot \beta +1}{\cot \theta -\cot \beta }}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8588f568e3859c1effc16e58090094a9f9a53659)
دوو ئەوەندەی گۆشە[دەستکاری]
![{\displaystyle \cos 2a=\cos ^{2}a-\sin ^{2}a=2\cos ^{2}a-1=1-2\sin ^{2}a\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1015c7eca3c2ede868a3f8a24cb84d416d9245f)
![{\displaystyle \sin 2a=2\sin a.\cos a\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9f226bcd1f4ff11078e991e24a582ff30b4397e)
![{\displaystyle \tan 2a={\frac {2\tan a}{1-\tan ^{2}a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8c53681f1c3272aad701a6e6fd154f90c1ccb9e)
![{\displaystyle \cot 2a={\frac {\cot ^{2}a-1}{2\cot a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/be74020d048be27445909eae78042f1213412d6b)
سێ ئەوەندەی گۆشە[دەستکاری]
![{\displaystyle \sin 3a=-\sin ^{3}a+3\cos ^{2}a\sin a=-4\sin ^{3}a+3\sin a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0d36d4925b64b01b62da936d104c4a74dce4bb)
![{\displaystyle \cos 3a=\cos ^{3}a-3\sin ^{2}a\cos a=4\cos ^{3}a-3\cos a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42ea0652281817df2ce01ad7472439fc945dfa1f)
![{\displaystyle \tan 3a={\frac {3\tan a-\tan ^{3}a}{1-3\tan ^{2}a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b847476896ded37cba790059d41fdbaaade96316)
![{\displaystyle \cot 3a={\frac {3\cot a-\cot ^{3}a}{1-3\cot ^{2}a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e93a7feb541cd40719cb593285583fb1a8a538e)
![{\displaystyle \cos a={\sqrt {{\frac {1}{2}}\ (1+\cos 2a)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb5a0d336395302115a3a268544fd23c02ef8f1c)
![{\displaystyle \sin a={\sqrt {{\frac {1}{2}}\ (1-\cos 2a)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b3ebaf741ed6534821030a94dad7a2770284a87c)
گۆڕینی لێکدان بە کۆکردنەوە[دەستکاری]
![{\displaystyle \cos a.\cos b={\frac {1}{2}}(\cos(a+b)+\cos(a-b))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0dea610bb87f27cebe5d703723ca3ab73acf340)
![{\displaystyle \sin a.\sin b={\frac {1}{2}}(\cos(a-b)-\cos(a+b))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9bf9e527a4f7a5cb625900edd79acc26682f74d5)
![{\displaystyle \sin a.\cos b={\frac {1}{2}}(\sin(a+b)+\sin(a-b))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d95ac69713ad818a5967b685b42e4e4aef4a223e)
گۆڕینی کۆکردنەوە بە لێکدان[دەستکاری]
![{\displaystyle \cos a+\cos b=2\cos {\frac {a+b}{2}}.\cos {\frac {a-b}{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0cc26a6b35e18ad8d51e86d3f7bb9513989ebe7)
![{\displaystyle \cos a-\cos b=-2\sin {\frac {a+b}{2}}.\sin {\frac {a-b}{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19e348c220a99d8442805ee4b2df8c52b6f46517)
![{\displaystyle \sin a+\sin b=2\sin {\frac {a+b}{2}}.\cos {\frac {a-b}{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95b4cccb6585983421ab7c928ade868b1dc1c89a)
![{\displaystyle \sin a-\sin b=2\cos {\frac {a+b}{2}}.\sin {\frac {a-b}{2}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44e031da2925f1bc674f8621cf8eb4aa1767e409)
کۆکردنەوەی ساین و کۆساینی گۆشە[دەستکاری]
![{\displaystyle \sin \theta +\cos \theta ={\sqrt {2}}\sin \left({\frac {\pi }{4}}+\theta \right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/119ed756451f1da0eca85e6ec10222e969c6a88f)
بەستەرە دەرەکییەکان[دەستکاری]