Bases

Question 1

( a + b )*2

Answer 1

a2 + 2ab + b2

Question 2

a2 + 2ab + b2

Answer 2

( a + b )*2

Question 3

( a - b )*2

Answer 3

a2 - 2ab + b2

Question 4

a2 - 2ab + b2

Answer 4

( a - b )*2

Question 5

(a + b) (a - b)

Answer 5

a2 - b2

Question 6

a2 - b2

Answer 6

(a + b) (a -b)

Question 7

a2 - b2

Answer 7

(a + b) (a -b)

Question 8

sin²(x) + cos²(x)

Answer 8

1

Question 9

sin(a - b)

Answer 9

sin(a)cos(b) - cos(a)sin(b)

Question 10

cos(a - b)

Answer 10

cos(a)cos(b) + sin(a)sin(b)

Question 11

tan(a + b)

Answer 11

(tan(a) + tan(b)) / (1 - tan(a)tan(b))

Question 12

tan(a - b)

Answer 12

(tan(a) - tan(b)) / (1 + tan(a)tan(b))

Question 13

sin(2a)

Answer 13

2 sin(a) cos(a)

Question 14

cos(2a)

Answer 14

cos²(a) - sin²(a) = 2cos²(a) - 1 = 1 - 2sin²(a)

Question 15

tan(2a)

Answer 15

(2 tan(a)) / (1 - tan²(a))

Question 16

sin²(a)

Answer 16

(1 - cos(2a)) / 2

Question 17

cos²(a)

Answer 17

(1 + cos(2a)) / 2

Question 18

sin(a)cos(b)

Answer 18

1/2 [sin(a + b) + sin(a - b)]

Question 19

cos(a)cos(b)

Answer 19

1/2 [cos(a + b) + cos(a - b)]

Question 20

sin(a)sin(b)

Answer 20

1/2 [cos(a - b) - cos(a + b)]

Question 21

cos(a) + cos(b)

Answer 21

2 cos((a + b)/2) cos((a - b)/2)

Question 22

cos(a) - cos(b)

Answer 22

-2 sin((a + b)/2) sin((a - b)/2)

Question 23

sin(a) + sin(b)

Answer 23

2 sin((a + b)/2) cos((a - b)/2)

Question 24

sin(a) - sin(b)

Answer 24

2 cos((a + b)/2) sin((a - b)/2)

Question 25

sin(a)cos(b)

Answer 25

1/2 [sin(a + b) + sin(a - b)]

Question 26

cos(a)cos(b)

Answer 26

1/2 [cos(a + b) + cos(a - b)]

Question 27

sin(a)sin(b)

Answer 27

1/2 [cos(a - b) - cos(a + b)]

Question 28

(sin x)'

Answer 28

cos x

Question 29

∫ sin x dx

Answer 29

-cos x + C

Question 30

(cos x)'

Answer 30

-sin x

Question 31

∫ cos x dx

Answer 31

sin x + C

Question 32

(tan x)'

Answer 32

1 / cos² x

Question 33

∫ tan x dx

Answer 33

ln|cos x| + C

Question 34

cosh(x)

Answer 34

(e^x + e^(-x)) / 2

Question 35

(cosh x)'

Answer 35

sinh x

Question 36

∫ cosh x dx

Answer 36

sinh x + C

Question 37

sinh(x)

Answer 37

(e^x - e^(-x)) / 2

Question 38

(sinh x)'

Answer 38

cosh x

Question 39

∫ sinh x dx

Answer 39

cosh x + C

Question 40

tanh(x)

Answer 40

sinh(x) / cosh(x)

Question 41

(tanh x)'

Answer 41

1 - tanh² x

Question 42

Qu'est-ce qu'une fonction paire ?

Answer 42

Une fonction f est paire si ∀x ∈ Df, f(-x) = f(x)

Question 43

Quelle est la symétrie d'une fonction paire ?

Answer 43

Elle est symétrique par rapport à l'axe des ordonnées.

Question 44

Qu'est-ce qu'une fonction impaire ?

Answer 44

Une fonction f est impaire si ∀x ∈ Df, f(-x) = -f(x).

Question 45

Quelle est la symétrie d'une fonction impaire ?

Answer 45

Elle est symétrique par rapport à l'origine du repère.

Question 46

(e^x)'

Answer 46

e^x

Question 47

(ln x)'

Answer 47

1/x

Question 48

(x^n)'

Answer 48

n * x^(n-1)

Question 49

(1/x)'

Answer 49

-1/x²

Question 50

Énonce le théorème de bijection.

Answer 50

Soit f une fonction continue et strictement monotone sur un intervalle I. Alors, f réalise une bijection de I sur son image J, et sa réciproque f⁻¹ est continue sur J.