Question

55 de puncte! va rog 4) calculaţi: a) sin136° cos44° + sin 44° cos 136° b)cos52° cos7° + sin52° sin7° 5) tg x + ctg x = 5/2 Demonstrați sin 2x = 0,8

Answer 1

Răspuns:

Explicație pas cu pas:

a) sin136° cos44° + sin 44° cos 136°=sin(136°+44°)=sin180°=0.

b) cos52° cos7° + sin52° sin7°=cos(52°-7°)=cos45°=√2/2.

$5)~~tgx+ctgx=\frac{5}{2},~\frac{sinx}{cosx} +\frac{cosx}{sinx}=\frac{5}{2},~\frac{sin^{2}x+cos^{2}x}{sinx*cosx}=\frac{5}{2},~=>~\frac{1}{sinx*cosx}=\frac{5}{2},~=>~\frac{sinx*cosx}{1} =\frac{2}{5}~|*2,~=>2sinx*cosx=\frac{4}{5},~=>~sin2x=0,8.$