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2.42 Appendix: Trigonometric addition rules

Trigonometric addition formulæ

sin⁡(x+y)=sin⁡x⁢cos⁡y+cos⁡x⁢sin⁡y,\sin(x+y)=\sin x\cos y+\cos x\sin y,
cos⁡(x+y)=cos⁡x⁢cos⁡y-sin⁡x⁢sin⁡y,\cos(x+y)=\cos x\cos y-\sin x\sin y,
sin⁡x+sin⁡y=2⁢sin⁡x+y2⁢cos⁡x-y2,\sin x+\sin y=2\sin{{x+y}\over{2}}\cos{{x-y}\over{2}},
cos⁡x+cos⁡y=2⁢cos⁡x+y2⁢cos⁡x-y2,\cos x+\cos y=2\cos{{x+y}\over{2}}\cos{{x-y}\over{2}},
cos⁡x-cos⁡y=2⁢sin⁡x+y2⁢sin⁡y-x2,\cos x-\cos y=2\sin{{x+y}\over{2}}\sin{{y-x}\over{2}},
tan⁡(x+y)=tan⁡x+tan⁡y1-tan⁡x⁢tan⁡y.\tan(x+y)={{\tan x+\tan y}\over{1-\tan x\tan y}}.