Explicație pas cu pas:
a) cos150°+cos30°)(sin120°-sin60°)
=(cos(180°-30°)+cos30°)(sin(180°-60°)-sin60°)
=(cos30°-cos30°)(sin60°-sin60°)=0*0=0
b)
tg²30°+tg²60°+ctg²45°+tg²0°=
=(√3/3)²+(√3/3)²+1²+0²=3/9+3/9+1=
=(3+3)/9+1=6/9+1=2/3+1=(2+3)/3=5/3
c)
(cos1°-cos9°)(cos2°-cos8°)*...*(cos9°-cos1°)=
(cos1°-cos9°)*(cos2°-cos8°)*(cos3°-cos7°)*(cos4°-cos6°)*(cos5°-cos5°)*
*(cos9°-cos1°)(cos8°-cos2°)(cos7°-cos3°)(cos6°-cos4°)(cos5°-cos5°)=
= --(cos1°-cos9°)²*(cos2°-cos8°)²*(cos3°-cos7°)(cos4°-cos6°)(cos5°-cos5°)=0
cos5°-cos5°=0 EVIDENT!
Bafta!
