Tabelas de engenharia/Identidades trigonométricas

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