Fonctions Classiques

Question 1

cos’(x)

Answer 1

-sin(x)

Question 2

arcos’(x)

Answer 2

-1/(1-x²)^1/2

Question 3

sin’(x)

Answer 3

cos(x)

Question 4

arcsin’(x)

Answer 4

1/(1-x²)^1/2

Question 5

tan’(x)

Answer 5

1/cos²(x) = 1 + tan²(x)

Question 6

arctan’(x)

Answer 6

1/(1+x²)

Question 7

ch’(x)

Answer 7

sh(x)

Question 8

argch(x)

Answer 8

ln(x + (x² -1)^1/2))

Question 9

argch’(x)

Answer 9

1/(x²-1)^1/2

Question 10

sh’(x)

Answer 10

ch(x)

Question 11

argsh(x)

Answer 11

ln(x+(x²+1)^1/2)

Question 12

argsh’(x)

Answer 12

1/(1+x²)^1/2

Question 13

th’(x)

Answer 13

1/ch²(x)

Question 14

argth(x)

Answer 14

1/2 x ln((1+x)/(1-x))

Question 15

argth’(x)

Answer 15

1/(1-x²)

Question 16

ch²+sh²

Answer 16

1

Question 17

Sh(2x)

Answer 17

2sh(x)ch(x)

Question 18

ch(2x)

Answer 18

ch²+sh²

Question 19

arccos(x) + arcsin(x)

Answer 19

π/2

Question 20

arctan(x) + arctan(1/x)

Answer 20

+/- π/2 selon le signe de x

Question 21

cos²(x)

Answer 21

(1+cos(2x))/2

Question 22

sin²(x)

Answer 22

(1-cos(2x))/2

Question 23

t = tan(x/2)

Answer 23

cos(x) = (1-t²)/(1+t²)

sin(x) = 2t/(1+t²)

tan(x) = 2t/(1-t²)

Question 24

cos(a+b)

Answer 24

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

Question 25

cos(a-b)

Answer 25

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

Question 26

2cos(a)cos(b)

Answer 26

cos(a+b) + cos (a-b)

Question 27

2sin(a)sin(b)

Answer 27

cos(a-b) - cos(a+b)

Question 28

sin(a+b)

Answer 28

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

Question 29

2sin(b)cos(a)

Answer 29

sin(a+b) - sin(a-b)

Question 30

sin(p) + sin(q)

Answer 30

2sin((p+q)/2)cos((p-q)/2)

Question 31

cos(p) + cos(q)

Answer 31

2cos((p+q)/2)cos((p-q)/2)

Question 32

tan(a+b)

Answer 32

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