1 ${\displaystyle \sin ^{2}\ +\ \cos ^{2}\ =\ 1}$ 15 ${\displaystyle 1\ +\ \tan ^{2}=\ \sec ^{2}}$ 2 ${\displaystyle \sin({\frac {\pi }{2}}-\theta )=\cos \theta }$ 16 ${\displaystyle \cos({\frac {\pi }{2}}-\theta )=\sin \theta }$ 3 ${\displaystyle \sec({\frac {\pi }{2}}-\theta )=\csc \theta }$ 17 ${\displaystyle \csc({\frac {\pi }{2}}-\theta )=\sec \theta }$ 4 ${\displaystyle \sin \ (-\theta )=\ -\sin \theta }$ 18 ${\displaystyle \cos \ (-\theta )=\sin \theta }$ 5 ${\displaystyle \sin 2\theta =\ 2\sin \theta \cos \theta }$ 19 ${\displaystyle \cos 2\theta =\ \cos ^{2}-\sin ^{2}=\ 2\cos ^{2}\theta \ -1=\ 1\ -2\sin ^{2}\theta }$ 6 ${\displaystyle \sin ^{2}\theta ={\frac {1-\cos 2\theta }{2}}}$ 20 ${\displaystyle \cos ^{2}\theta ={\frac {1+\cos 2\theta }{2}}}$ 7 ${\displaystyle \sin \alpha +\sin \beta =2\sin({\frac {\alpha +\beta }{2}})\cos({\frac {\alpha -\beta }{2}})}$ 21 ${\displaystyle \sin \alpha -\sin \beta =2\cos({\frac {\alpha +\beta }{2}})\sin({\frac {\alpha -\beta }{2}})}$ 8 ${\displaystyle \cos \alpha +\cos \beta =2\cos({\frac {\alpha +\beta }{2}})\cos({\frac {\alpha -\beta }{2}})}$ 22 ${\displaystyle \cos \alpha -\cos \beta =-2\sin({\frac {\alpha +\beta }{2}})\sin({\frac {\alpha -\beta }{2}})}$ 9 ${\displaystyle \sin \alpha \sin \beta ={\frac {1}{2}}[\cos(\alpha -\beta )-\cos(\alpha +\beta )]}$ 23 ${\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}[\cos(\alpha -\beta )+\cos(\alpha +\beta )]}$ 10 ${\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}[\sin(\alpha +\beta )+\sin(\alpha -\beta )]}$ 24 ${\displaystyle 1\ +\cot ^{2}=\csc ^{2}}$ 11 ${\displaystyle e^{j\theta }\ =\cos \theta +\ j\sin \theta }$ 25 ${\displaystyle \cos \theta ={\frac {e^{j\theta }+e^{-j\theta }}{2}}}$ 12 ${\displaystyle \tan({\frac {\pi }{2}}-\theta )=\cot \theta }$ 26 ${\displaystyle \cot({\frac {\pi }{2}}-\theta )=\tan \theta }$ 13 ${\displaystyle \tan(-\theta )\ =\cot \theta }$ 27 ${\displaystyle \tan 2\theta ={\frac {2\tan \theta }{1-tan^{2}\theta }}}$ 14 ${\displaystyle \tan ^{2}\theta ={\frac {1-\cos 2\theta }{1+\cos 2\theta }}}$ 28 ${\displaystyle \sin \theta ={\frac {e^{j\theta }-e^{-j\theta }}{j2}}}$