Trig Identities

Question 1

Reciprocal ID:

cos(x) =

Answer 1

1 / sec(x)

Question 2

Reciprocal ID:

sin(x) =

Answer 2

1 / csc(x)

Question 3

Reciprocal ID:

tan(x) =

Answer 3

sin(x) / cos(x) = 1 / cot(x)

Question 4

Reciprocal ID:

cot(x) =

Answer 4

cos(x) / sin(x) = 1 / tan(x)

Question 5

Reciprocal ID:

sec(x) =

Answer 5

1 / cos(x)

Question 6

Reciprocal ID:

csc(x) =

Answer 6

1 / sin(x)

Question 7

Cofunction ID:

cos((π / 2) - x) =

Answer 7

sin(x)

Question 8

Cofunction ID:

tan((π / 2) - x) =

Answer 8

cot(x)

Question 9

Cofunction ID:

sec((π / 2) - x) =

Answer 9

csc(x)

Question 10

Cofunction ID:

sin((π / 2) - x) =

Answer 10

cos(x)

Question 11

Cofunction ID:

cot((π / 2) - x) =

Answer 11

tan(x)

Question 12

Cofunction ID:

csc((π / 2) - x) =

Answer 12

sec(x)

Question 13

Pythagorean ID:

1 =

sin

Answer 13

cos ² (x) + sin ² (x)

Question 14

Pythagorean ID:

1 =

tan

Answer 14

tan ² (x) + sec ² (x)

Question 15

Pythagorean ID:

1 =

cot

Answer 15

cot ² (x) + csc ² (x)

Question 16

Double Angle ID:

sin2x =

Answer 16

2sinxcosx

Question 17

Double Angle ID:

cos2x =

Answer 17

cos ² (x) - sin ² (x) =
cos ² (x) - sin ² (x) =
2cos ² (x) - 1 =
1 - 2sin ² (x)

Question 18

Pythagorean ID

tan2x =

Answer 18

2tanx / (1 - tan ² (x))

Question 19

Sum and Difference ID:

cos(A +/- B) =

Answer 19

cosAcosB -/+ sinAsinB

Question 20

Sum and Difference ID:

sin(A +/- B) =

Answer 20

sinAcosB +/- cosAsinB

Question 21

Sum and Difference ID:

tan(A +/- B) =

Answer 21

(tanA +/- tanB) / (1 -/+ tanAtanB)

Question 22

Product-to-Sum ID:

cosAcosB =

Answer 22

(cos(A - B) + cos (A + B)) / 2

Question 23

Product-to-Sum ID:

sinAsinB =

Answer 23

(cos(A - B) - cos (A + B)) / 2

Question 24

Product-to-Sum ID:

sinAcosB =

Answer 24

(sin(A + B) + sin (A - B)) / 2

Question 25

Power-Reduction Formula:

cos ² (x) =

Answer 25

(1 + cos2x) / 2

Question 26

Power-Reduction Formula:

sin ² (x) =

Answer 26

(1 - cos2x) / 2