Question

♥ Задание во вложении ♥

Answer 1

$1)\; \; tga=-\frac{3}{4}=-0,75\; \; ,\; \; tg\beta =2,4\\\\\\tg(a+\beta )=\dfrac{tga+tg\beta }{1-tga\cdot tg\beta }=\dfrac{-0,75+2,4}{1+0,75\cdot 2,4}=\dfrac{1,65}{2,8}=\dfrac{165}{280}=\dfrac{33}{56}$

$2)\; \; 1+2sina=2\cdot (\frac{1}{2}+sina)=2\cdot (sin\frac{\pi}{6}+sina)=\\\\=2\cdot 2\cdot sin(\frac{\pi}{12}+\frac{a}{2})\cdot cos(\frac{\pi}{12}-\frac{a}{2})=4\cdot sin(\frac{\pi}{12}+\frac{a}{2})\cdot cos(\frac{\pi}{12}-\frac{a}{2})$

$3)\; \; \dfrac{2\cdot (cosa+cos3a)}{2\cdot sin2a+sin4a}=\dfrac{4\cdot cos2a\cdot cosa}{2\cdot sin2a+2\cdot sin2a\, cos2a}=\\\\\\=\dfrac{4\cdot cos2a\cdot cosa}{2\, sin2a\cdot (1+cos2a)}=\dfrac{2\cdot cos2a\cdot cosa}{sin2a\cdot 2cos^2a}=\dfrac{cos2a}{sin2a\cdot cosa}=\dfrac{ctga}{cosa}$