Question

Aduceți la o forma mai simpla expresia:

Answer 1

expresia pare a fi
2cos2α+2sin(α+30°)sin(α-30°)

in acest caz,
ne amintim cos (α+β)=cosαcosβ-sinαsinβ
atunci
 sinαsinβ=-cos(α+β)+cosαcosβ
dac α+30°->α
si α-30°->β
avem

2cos2α+2sin(α+30°)sin(α-30°)=

2 cos2α+2[-cos(α+30°+α-30)+cos(α+30°)cos(α-30°)]=
2cos2α-2cos2α+2cos(α+30°)*cos(α-30°)=
=2cos(α+30°)cos(α-30°)
acum
transformam produsul in suma (formula am luat-o din tabele, nu am tinut-o minte, spre deosebirede prima, cos (α+β), fundamentala, pe care o stiam)

= 2* [cos(α+30°+α-30°)+cos(α+30°-α+30°)]/2
=cos2α+cos60°=cos2α+1/2