Trigonometrijas formulas matemātikas eksāmena formulu lapā

$\begin{array}{l}{\mathrm{sin}}^{2}\mathrm{\alpha }+{\mathrm{cos}}^{2}\mathrm{\alpha }=1\\ \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }=\frac{\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}{\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathrm{ctg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }=\frac{\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}{\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}\\ \phantom{\rule{0.147em}{0ex}}\\ 1+{\mathrm{tg}}^{2}\mathrm{\alpha }=\frac{1}{{\mathrm{cos}}^{2}\mathrm{\alpha }}\\ 1+{\mathrm{ctg}}^{2}\mathrm{\alpha }=\frac{1}{{\mathrm{sin}}^{2}\mathrm{\alpha }}\\ \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{ctg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }=1\\ \\ \mathrm{sin}\phantom{\rule{0.147em}{0ex}}2\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}2\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}{\mathrm{cos}}^{2}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}{\mathrm{sin}}^{2}\mathrm{\alpha }\\ \mathrm{tg}\phantom{\rule{0.147em}{0ex}}2\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{2\phantom{\rule{0.147em}{0ex}}\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}{1\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}{\mathrm{tg}}^{2}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }}\\ \\ \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }±\mathrm{\beta }\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}±\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }+\mathrm{\beta }\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }-\mathrm{\beta }\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\\ \\ \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }+\mathrm{\beta }\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }+\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }}{1\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }}\\ \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }-\mathrm{\beta }\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }-\phantom{\rule{0.147em}{0ex}}\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }}{1\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}\mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{tg}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }}\end{array}$

$\begin{array}{l}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}+\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }+\mathrm{\beta }}{2}\cdot \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }-\mathrm{\beta }}{2}\\ \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}-\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }-\mathrm{\beta }}{2}\cdot \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }+\mathrm{\beta }}{2}\\ \\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }+\mathrm{\beta }}{2}\phantom{\rule{0.147em}{0ex}}\cdot \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }-\mathrm{\beta }}{2}\\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }\phantom{\rule{0.147em}{0ex}}=-\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }+\mathrm{\beta }}{2}\phantom{\rule{0.147em}{0ex}}\cdot \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\frac{\mathrm{\alpha }-\mathrm{\beta }}{2}\\ \\ \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathit{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }=\frac{\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }-\mathrm{\beta }\right)+\mathrm{sin}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }+\mathrm{\beta }\right)}{2}\\ \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{sin}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }=\frac{\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }-\mathrm{\beta }\right)-\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }+\mathrm{\beta }\right)}{2}\\ \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\alpha }\cdot \mathrm{cos}\phantom{\rule{0.147em}{0ex}}\mathrm{\beta }=\frac{\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }-\mathrm{\beta }\right)+\mathrm{cos}\phantom{\rule{0.147em}{0ex}}\left(\mathrm{\alpha }+\mathrm{\beta }\right)}{2}\end{array}$