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Simplifier les expressions suivantes :
A = 1 + 2 cos a + cos 2a
B = 1 + 2 sin a - cos 2a
C = ( 1 - cos a + sin a ) / ( 1 + cos a + sin a )
Merci
Simplifier les expressions suivantes :
A = 1 + 2 cos a + cos 2a
B = 1 + 2 sin a - cos 2a
C = ( 1 - cos a + sin a ) / ( 1 + cos a + sin a )
Merci
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Verified answer
A = 1 + 2 cos a + cos 2a=1+2cos(a)+2cos²(a)-1
=(2cos(a))(1+cos(a))
B = 1 + 2 sin a - cos 2a
=1-2sin(a)-(2cos²(a)-1)
=2(sin(a)-cos²(a))
C = ( 1 - cos a + sin a ) / ( 1 + cos a + sin a )
=(1-cos a+sin a)²/((1+cos a)²-(sin a)²)
=(1+cos²(a)+sin²(a)-2cos(a)+2sin(a)-sin(2a))/(1+cos²(a)-2cos(a)-sin²(a))
=tan(a/2)