Question

sin2 30+sin2 45+sin2 60

Answer 1

Răspuns:

=3/2

Explicație pas cu pas:

sin 30°=1/2 ⇒ sin² 30°=(1/2)²=1/4

sin 45°=√2/2 ⇒ sin² 45°=(√2/2)²=2/4

sin 60°=√3/2 ⇒ sin² 60°=(√3/2)²=3/4

sin² 30° +sin² 45°+sin² 60°=1/4 + 2/4 + 3/4=6/4=3/2

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sin (2·30°)+sin(2·45°)+sin(2·60°)=

=sin 60° +sin 90° + sin 120°=

=√3/2 + 1 + sin(180°-120°)=

=√3/2 + 1 + sin 60°=

=√3/2 + 1 +√3/2=

=1+√3

Answer 2

sin²30° + sin²45° + sin²60° =

= sin²30° + sin²45° + sin²(90°-30°) =

= sin²30° + sin²45° + cos²30° =

= sin²30° + cos²30° + sin²45° =

= 1 + sin²45° =

= 1+ [(√2)/2)² =

= 1 + 2/4 =

= 1 + 1/2 =

= 3/2