Question

Va rog mult ,acolo unde e ingrosat e 30° si la sfarsit la 0 e semul de °

Answer 1

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!