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Nouhaila43
@Nouhaila43
May 2019
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Bonsoir (Pour la démonstration du cos j'ai eu un + et un - mais pour prouver que c'est positive j'ai essayé d'utiliser la tan car √2-1>0 "est ce que c juste)
sachant que tanπ/8=√2-1
montrer que cosπ/8=\sqrt{2+\sqrt{2}} /2 et calculer sinπ/8
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ProfdeMaths1
Verified answer
Tan(π/8)=√2-1
cos²(π/8)=1/(tan²(π/8)+1)
=1/((√2-1)²+1)
=1/(2-2√2+1+1)
=1/(4-2√2)
=(4+2√2)/(4²-(2√2)²)
=(4+2√2)/8
=(2+√2)/4
0<π/8<π/2 ⇒ cos(π/8)=√((2+√2)/4)=1/2.√(2+√2)
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Verified answer
Tan(π/8)=√2-1cos²(π/8)=1/(tan²(π/8)+1)
=1/((√2-1)²+1)
=1/(2-2√2+1+1)
=1/(4-2√2)
=(4+2√2)/(4²-(2√2)²)
=(4+2√2)/8
=(2+√2)/4
0<π/8<π/2 ⇒ cos(π/8)=√((2+√2)/4)=1/2.√(2+√2)