Тригонометрические формулы. Профильный ЕГЭ, часть 1

\(\sin ^{2}\alpha + \cos ^{2}\alpha =1\)

\(\textup{tg}^{2}\alpha +1=\displaystyle \frac{1}{\cos ^{2}\alpha }\)

\(1+ \textup{ctg}^{2}\alpha =\displaystyle \frac{1}{\sin ^{2}\alpha }\)

\(\sin(\alpha +\beta )=\sin \alpha \cos b+\cos \alpha \sin \beta \)
\(\sin(\alpha -\beta )=\sin \alpha \cos b-\cos \alpha \sin \beta \)
\(\cos(\alpha +\beta )=\cos \alpha \cos b-\sin \alpha \sin \beta \)
\(\cos(\alpha -\beta )=\cos \alpha \cos b+\sin \alpha \sin \beta \)

\(sin 2 \alpha =2 \sin \alpha \cos \alpha \)
\(\cos 2\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha \)
\(\cos 2\alpha =2\cos ^{2}\alpha -1\)
\(\cos 2\alpha =1- 2\sin^{2} \alpha\)

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

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