Identidades

Question 1

Cos^2 (x) + sin^2 (x) =

Answer 1

1

Question 2

Sec^2 (x) - tan^2 (x) =

Answer 2

1

Question 3

Csc^2 (x) - cot^2 (x) =

Answer 3

1

Question 4

1

Answer 4

Cos^2 (x) + sin^2 (x) = 1

Sec^2 (x) - tan^2 (x) = 1

Csc^2 (x) - cot^2 (x) = 1

Question 5

Sin (x) =

Answer 5

+/- Raiz (1-cos^2 (x) )

1/ csc (x)

Question 6

+/- Raiz (1-cos^2 (x) ) =

Answer 6

Sin (x)

Question 7

Cos ( x) =

Answer 7

+/- raiz ( 1- sin^2 (x))

1/ sec x

Question 8

+/- raiz ( 1- sin^2 (x))=

Answer 8

Cos (x)

Question 9

Sin (x +/- y ) =

Answer 9

Sin x cos y +/- cos x sin y

Question 10

Sin x cos y +/- cos x sin y=

Answer 10

Sin (x +/- y )

Question 11

Cos ( x +/- y ) =

Answer 11

Cos (x) cos (y) -/+ sin (x) sin (y)

Question 12

Cos (x) cos (y) -/+ sin (x) sin (y)=

Answer 12

Cos ( x +/- y )

Question 13

Tan ( x +/- y ) =

Answer 13

= (tan (x) +/- tan (y) ) / ( 1 -/+ tan (x) tan (y)

Question 14

(tan (x) +/- tan (y) ) / ( 1 -/+ tan (x) tan (y) =

Answer 14

Tan ( x +/- y )

Question 15

Csc ( x +/- y ) =

Answer 15

1/ (sin (x +/- y )

Question 16

1/ (sin (x +/- y ) =

Answer 16

Csc ( x +/- y )

Question 17

Sec (x +/- y ) =

Answer 17

= 1/ ( cos ( x +/- y )

Question 18

1/ ( cos ( x +/- y ) =

Answer 18

Sec (x +/- y )

Question 19

Cot ( x +/- y ) =

Answer 19

= (cot x cot y - /+ 1 ) / ( cot y + /- cot x )

Question 20

(cot x cot y - /+ 1 ) / ( cot y + /- cot x ) =

Answer 20

Cot ( x +/- y )

Question 21

Sin 2x

Answer 21

Sin 2x

= 2 sin x cos x

Question 22

= 2 sin x cos x

Answer 22

Sin 2x

Question 23

Cos 2x

Answer 23

Cos 2x 
= 1- tan^2 x / 1 + tan^2 x 
= cos^2 x - sin^2 x
= 2 cos^2 x - 1 
= 1 - 2 sin^2 x

Question 24

= 1- tan^2 x / 1 + tan^2 x
= cos^2 x - sin^2 x
= 2 cos^2 x - 1
= 1 - 2 sin^2 x

Answer 24

Cos 2x

Question 25

Tan 2x

Answer 25

Tan 2x | = 2 tan x / 1- tan^2 x

Question 26

2 tan x / 1- tan^2 x =

Answer 26

Tan 2x

Question 27

Cot 2x

Answer 27

Cot 2x | =( cot^2 x - 1 ) / 2 cot x

Question 28

( cot^2 x - 1 ) / 2 cot x=

Answer 28

Cot 2x

Question 29

Sin x/ 2 =

Answer 29

Sin x/ 2 = +/- raiz ( 1- cos x / 2 )

Question 30

+/- raiz ( 1- cos x / 2 ) =

Answer 30

Sin x/ 2

Question 31

+/- raiz ( 1 + cos x / 2 ) =

Answer 31

Cos x/2 = | +/- raiz ( 1 + cos x / 2 )

Question 32

+/- raiz ( 1 + cos x / 2 ) =

Answer 32

Cos x/2 =

Question 33

Tan x/2

Answer 33

Tan x/2 = sin x / 1 + cos x = 1- cos x / sin x

Question 34

= 1- cos x / sin x | = sin x / 1 + cos x

Answer 34

Tan x/2

Question 35

Sin x =

Answer 35

1 / csc x

Question 36

Cos x =

Answer 36

1 / sec x

Question 37

Tan x =

Answer 37

1 / cot x | Sen x / cos x

Question 38

Cot x =

Answer 38

1 / tan x

Question 39

Sec x =

Answer 39

1 / cos x

Question 40

Csc x =

Answer 40

1 / sin x