Question

Вычислите (tg a-ctd a) : (sin a - cos a), если sin a+ cos a=1,2

Answer 1

$(tga-ctga):(sina-cosa)=(frac{sina}{cosa}-frac{cosa}{sina}):(sina-cosa)=\\=frac{sin^2a-cos^2a}{sinacdot cosa}cdot frac{1}{sina-cosa}=frac{(sina-cosa)(sina+cosa)}{sinacdot cosacdot (sina-cosa)}=frac{sina+cosa}{sinacdot cosa}=\\=frac{1,2}{sinacdot cosa}=frac{1,2}{0,22}=frac{120}{22}=frac{60}{11}=5frac{5}{11}\\\star ; ; sina+cosa=1,2\\(sina+cosa)^2=1,44\\sin^2a+2sinacdot cosa+cos^2a=1,44\\1+2sinacdot cosa=1,44\\2sinacdot cosa=1,44-1\\2sinacdot cosa=0,44\\sinacdot cosa=0,22$