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Appendix B List of Trigonometric Identities
\(\displaystyle [\sin(\alpha)]^2+[\cos(\alpha)]^2=1\)
\(\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)\)
\(\displaystyle \sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)\)
\(\displaystyle \cos(2\alpha) = [\cos(\alpha)]^2-[\sin(\alpha)]^2 = 2[\cos(\alpha)]^2-1 = 1-2[\sin(\alpha)]^2\)
\(\displaystyle \sin(2\alpha)=2\sin(\alpha)\cos(\alpha)\)
\(\displaystyle [\cos(\alpha)]^2=\displaystyle\frac{1+\cos(2\alpha)}{2}\)
\(\displaystyle [\sin(\alpha)]^2=\displaystyle\frac{1-\cos(2\alpha)}{2}\)
\(\displaystyle \sin(\alpha)\cos(\beta)=\displaystyle\frac{\sin(\alpha+\beta)+\sin(\alpha-\beta)}{2}\)
\(\displaystyle \sin(\alpha)\sin(\beta)=\displaystyle\frac{\cos(\alpha-\beta)-\cos(\alpha+\beta)}{2}\)
\(\displaystyle \cos(\alpha)\sin(\beta)=\displaystyle\frac{\sin(\alpha+\beta)-\sin(\alpha-\beta)}{2}\)
\(\displaystyle \cos(\alpha)\cos(\beta)=\displaystyle\frac{\cos(\alpha-\beta)+\cos(\alpha+\beta)}{2}\)
\(\displaystyle \sin(\alpha)+\sin(\beta)=2\sin\left(\displaystyle\frac{\alpha+\beta}{2}\right)\cos\left(\displaystyle\frac{\alpha-\beta}{2}\right)\)
\(\displaystyle \sin(\alpha)-\sin(\beta)=2\cos\left(\displaystyle\frac{\alpha+\beta}{2}\right)\sin\left(\displaystyle\frac{\alpha-\beta}{2}\right)\)
\(\displaystyle \cos(\alpha)+\cos(\beta)=2\cos\left(\displaystyle\frac{\alpha+\beta}{2}\right)\cos\left(\displaystyle\frac{\alpha-\beta}{2}\right)\)
\(\displaystyle \cos(\alpha)-\cos(\beta)=-2\sin\left(\displaystyle\frac{\alpha+\beta}{2}\right)\sin\left(\displaystyle\frac{\alpha-\beta}{2}\right)\)
