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1?re.S
Trigonom?trie/S2
Exercice I Soit x R, On pose: Ax cos 2x cos x sin x
1. Montrer que: Ax cos x sin x1 cos x sin x
Prof: Maghnouj
2.
D?duire
que:
Ax 2cos x
4
2 2
sin x
4
3. R?soudre dans R l'?quation: Ax 0
Exercice II
Soit x R, On pose:
Ax
cos3
x
sin3
x
32 4
sin x
4
1. Montrer que: cos3 x sin3 x 1 sin x cos x2 sin2x
2
2.
a)
Montrer
que:
Ax
1
2
sin x
cos
x
1 2
sin
2x
b) D?duire que: Ax
2 2
cos
x
4
1 2
sin
2x
3. R?soudre dans ,2l'?quation: Ax 0
Exercice III Soit x R, On pose: Ax 2cos3 x 2sin2 x. cos x cos x sin x
1. Montrer que: Ax cos x sin xcos2x sin2x
2.
D?duire
que:
Ax
2cos x
4
.
sin 2x
4
3. R?soudre dans 0, l'?quation: Ax 0
Exercice IV Soit x R, On pose: Ax 2cos3 x 2sin3 x cos x 2 sin x
1.
Montrer
que:
Ax
2
sin
x 2
sin
3x 2
sin
x 2
et
sin x 2sin3 x 1 cos x.sin2x 2
2. Montrer que: Ax
2
cos
2x
4
.
cos
x
3. R?soudre dans , l'?quation: Ax 0 Exercice IV Soit x R, On pose: Ax 1 2cos x cos2x et B x 1 2cos x cos2x
1. Montrer que: 2cos3 x cos x cos2x.cos x
et
Bx
2 cos
x 2
cos
3x 2
cos
x 2
2. Montrer que:
Ax
4 sin2
x 2
cos x
et
Bx
4 cos2
x 2
cos x
3. R?soudre dans R les ?quations : Ax 0 et B x 0
4. 3. R?soudre dans R les ?quations : Bx Ax
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