Question

Arătați că sin^2 120 grade -cos^2 30 grade =0

Answer 1

sin(180°-x)=sin x

Deci sin 120°=sin(180°-120°)=sin 60°=√3/2.

Atunci:

sin²120°=(√3/2)²=3/4

cos 30°=√3/2

cos²30°=3/4

Finalizand:

sin²120°-cos²30°=3/4-3/4=0

Answer 2

Folosim formula:

sin(90°+x) = cos(x)

Rezolvare:

sin²(120°) - cos²(30°) = 
= sin²(90°+30°) - cos²(30°) 
= cos²(30°) - cos²(30°)
= 0