Question

Найдите tg2a,если cosa=-(4/5) и пи<а<3пи/2

Answer 1

$cosa=-\frac{4}{5}\\\\\pi <a<\frac{3\pi}{2}\; \; \to \; \; sina<0\; ,\; tga>0\\\\sina=-\sqrt{1-cos^2a}=-\sqrt{1-\frac{16}{25}}=-\frac{3}{5}\\\\tga=\frac{sina}{cosa}=-\frac{3}{5}:(-\frac{4}{5})=\frac{3}{4}\\\\tg2a=\frac{2tga}{1-tg^2a}=\frac{2\cdot \frac{3}{4}}{1-\frac{9}{16}}=\frac{3}{2\cdot \frac{7}{16}}=\frac{3\cdot 8}{7}=\frac{24}{7}=3\frac{3}{7}$