Question

Pentru a transforma in produs expresia 1+cos a putem proceda in doua moduri :
1+cos a =cos0+cos a =2cos 0+a/2 *cos 0-a/2=2 cos 2a/2.

1+cos a =1+cos2 a/2-sin2 a/2=2 cos2 a/2.
a)Deduceti in doua moduri formula 1-cos a =2sin2 a/2.
b)Transformati in produs expresiile 1+sin a, 1 -sin a.

Answer 1

sin^2 + cos^2 =1
a)1-cosa=1-(cos(a/2))^2+(sin(a/2))^2=2(sin(a/2))^2 
 1-cosa=cos0+cosa=2(cos((0+a)/2)(cos((0-a)/2)=2(cos(a/2))^2
b)  1+sina= sin(pi/2)+sina=2sin((pi+a)/2)sin((pi-a)/2) 
 1-sina= sin(pi/2)-sina=2sin((pi+a)/2)cos((pi-a)/2)