Question

Calculați :
sin30°×cos30°+tg60°×ctg60°+sin45°×cos45°-sin60°×cos60°

Answer 1

1/2*√3/2+1/√3*√3+√2/2*√2/2-√3/2*1/2=√3/4+1+2/4-√3/4=1+1/2=3/2

Answer 2

   
sin30° × cos30° - sin60° × cos60° = 0
deoarece  sin30°  =  cos60°   si   cos30°  =  sin60°, 
unghiurile de 30°  si  60°  fiind complementare.

Ramanem cu:
tg60° × ctg60° + sin45° × cos45° = ?

Stim ca:
tg60°  = √3
ctg60° = √3 / 3
sin45° = cos45°  = √2 / 2

⇒  tg60° × ctg60° + sin45° × cos45° = 
  =  √3  ×  (√3 / 3)   +  (√2 / 2)  ×  (√2 / 2) = (3 / 3) + (2 / 4) = 1+ 1/2 = 3/2