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1-calculer
(2cos(x)+3sin(x))²+(3cos(x)-2sin(x))²
2-calculer
A=cos(5π/12)+cos(π/12)+cos(7π/12)+cos(11π/12)
B=cos²(π/6)+cos²(3π/8)+cos²(5π/8)+cos²(7π/8)
C=tan(π/5+tan(2π/5)+tan(3π/5)+tan(4π/5)
D=1+sin(π/7)+sin(2π/7)+.......+sin(13π/7)
3-soit x appartient a l'ensemble R tel que :cos(x)+sin(x)=4/5
calculer cos(x)*sin(x) et 1/cos(x)+1/sin(x)
4-simplifier les expressions suivantes
E=sin(15π-x)-cos(5π/2-x)-sin(5π-x)*cos(5π-x)
F=sin(11π-x)+cos(5π+x)+cos(14π-x)-sin(9π/2-x)
1-calculer
(2cos(x)+3sin(x))²+(3cos(x)-2sin(x))²
2-calculer
A=cos(5π/12)+cos(π/12)+cos(7π/12)+cos(11π/12)
B=cos²(π/6)+cos²(3π/8)+cos²(5π/8)+cos²(7π/8)
C=tan(π/5+tan(2π/5)+tan(3π/5)+tan(4π/5)
D=1+sin(π/7)+sin(2π/7)+.......+sin(13π/7)
3-soit x appartient a l'ensemble R tel que :cos(x)+sin(x)=4/5
calculer cos(x)*sin(x) et 1/cos(x)+1/sin(x)
4-simplifier les expressions suivantes
E=sin(15π-x)-cos(5π/2-x)-sin(5π-x)*cos(5π-x)
F=sin(11π-x)+cos(5π+x)+cos(14π-x)-sin(9π/2-x)
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Verified answer
1) calculer(2 cos(x) + 3 sin (x))² + (3 cos(x) - 2 sin (x))²
4 cos²(x) + 12 cos(x)sin(x) + 9 sin² (x) + 9 cos²(x) - 12 cos(x)sin(x) + 4 sin²(x)
13 cos²(x) + 13 sin²(x) = 13(cos²(x) + sin²(x)) = 13
car cos²(x) + sin²(x) = 1
2) calculer
A = cos(5π/12) + cos(π/12) + cos(7π/12) + cos(11π/12)
5π/12 = π/2 - π/12 ⇒ cos(π/2 - π/12) = sin (π/12)
7π/12 = π/2 + π/12 ⇒ cos(π/2 + π/12) = - sin (π/12)
11π/12 = π - π/12 ⇒ cos(π - π/12) = - cos (π/12)
A = cos(π/2 - π/12) + cos(π/2 + π/12) + cos(π - π/12)
= sin (π/12) - sin (π/12) - cos (π/12)
= - cos (π/12) = - 0.966
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