Question 194692
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Sum and difference formulae:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(\alpha \pm \beta) = \sin{\alpha}\cos{\beta}\pm\cos{\alpha}\sin{\beta}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(\alpha \pm \beta) = \cos{\alpha}\cos{\beta}\mp\sin{\alpha}\sin{\beta}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin{2\alpha} = \sin(\alpha + \alpha) = \sin{\alpha}\cos{\alpha}+\cos{\alpha}\sin{\alpha} = 2\sin{\alpha}\cos{\alpha}]


And:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos{2\alpha}=\cos(\alpha + \alpha) = \cos{\alpha}\cos{\alpha}-\sin{\alpha}\sin{\alpha} = \cos^2{\alpha} - \sin^2{\alpha}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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