trigonometrie

Question 1

sin(x+y)

Answer 1

sin x * cos y + sin b * cos a

Question 2

sin(x-y)

Answer 2

sin x * cos y - sin b * cos a

Question 3

cos(x+y)

Answer 3

cos x * cos y - sin x * sin y

Question 4

cos(x-y)

Answer 4

cos x * cos y + sin x * sin y

Question 5

cos2x

Answer 5

cos^2 x - sin^2 x
1- 2sin^2 x
2cos^2 x -1

Question 6

sin2x

Answer 6

2 sin x * cos x

Question 7

tg(x+y)

Answer 7

tg x + tg y/1 - tg x * tg y

Question 8

tg (x-y)

Answer 8

tg x - tg y/1+ tg x * tg y

Question 9

ctg(x+y)

Answer 9

ctg x * ctg y -1/ ctg x + ctg y

Question 10

ctg(x-y)

Answer 10

ctg x * ctg y +1/ ctg x - ctg y

Question 11

tg 2x

Answer 11

2tg x/ 1- tg^2 x

Question 12

ctg 2x

Answer 12

ctg^2 x - 1/ 2 ctg x

Question 13

cos 3x

Answer 13

cos x(4 cos ^2 x -3)

Question 14

sin 3x

Answer 14

sin x( 3 - 4 sin^2)

Question 15

sin( arccos x)

Answer 15

sqrt 1- x^2

Question 16

cos ( arcsin x)

Answer 16

sqrt 1- x^2

Question 17

arcsin x + arccos x

Answer 17

pi/2

Question 18

arctg x+ arcctg x

Answer 18

pi/2

Question 19

sin x + sin y

Answer 19

2 sin x+y/2 * cos x-y/2

Question 20

sin x - sin y

Answer 20

2 sin x- y/2 * cos x+y/2

Question 21

cos x + cos y

Answer 21

2 cos x+y/2 * cos x-y/2

Question 22

cos x - cos y

Answer 22

2 sin x - y/2 * sin x+y/2

Question 23

sin * sin y

Answer 23

cos(x-y) + cos (x+y)/2

Question 24

sin x * cos y

Answer 24

sin(x+y) + son(x-y)/2

Question 25

cos x * cos y

Answer 25

cos (x+y) + cos (x-y)/2

Question 26

sin(-x)

Answer 26

-sinx

Question 27

cos(-x)

Answer 27

cosx

Question 28

tg(-x)

Answer 28

-tgx

Question 29

ctg(-x)

Answer 29

-ctgx

Question 30

arcsin(-x)

Answer 30

-arcsinx

Question 31

arccos(-x)

Answer 31

pi-arccosx

Question 32

arctg(-x)

Answer 32

-arctgx

Question 33

arcctg(-x)

Answer 33

pi-arcctgx

Question 34

sinx=a

Answer 34

x apartine {(-1)^k arcsin x + kpi, k apartine lui Z}

Question 35

cosx=a

Answer 35

x apartine {plus, minus 1 arcos x + 2kpi, k apartine lui Z

Question 36

tgx=a

Answer 36

x apartine { arctg x + kpi, k apartine lui Z}

Question 37

ctgx=a

Answer 37

x apartine {arcctg x + kpi}