Question

♥ Задание во вложении ♥

Answer 1

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

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

$3); ; dfrac{2cdot (cosa+cos3a)}{2cdot sin2a+sin4a}=dfrac{4cdot cos2acdot cosa}{2cdot sin2a+2cdot sin2a, cos2a}=\\\=dfrac{4cdot cos2acdot cosa}{2, sin2acdot (1+cos2a)}=dfrac{2cdot cos2acdot cosa}{sin2acdot 2cos^2a}=dfrac{cos2a}{sin2acdot cosa}=dfrac{ctga}{cosa}$