Question

Calculati :
a) sin 25 x cos 35 + sin 35 x cos 25
b) cos 12 x cos 18 - sin 12 x sin 18
c) cos 80 x cos 35 + sin 80 x sin 35

Answer 1

Vezi formulele ptr sin x sin, sin x cos si cos x cosSe tine cont ca sin(-a) = -sin(a) si cos(-a)=cos(a)a)sin25xcos35=1/2(sin(25+35)+sin(25-35))=sin60-sin10=(1/2)xrad3/2-sin10sin35xcos25=1/2(sin(35+25)+sin(35-25))=sin69+sin10=(1/2)xrad3/2+sin10Adunand rezulta : rad3/2b)cos12xcos18=1/2(cos(30)+cos(-6))=1/2xrad3/2+cos6sin12xsin18=1/2(cos(-6)-cos(30))=-1/2xrad3/2+cos6Scazand rezulta : rad3/2c)Analog cu b)