Trig Identities

Question 1

sin(A+B)

Answer 1

sin(A)cos(B) + cos(A)sin(B)

Question 2

sin(A-B)

Answer 2

sin(A)cos(B) - cos(A)sin(B)

Question 2

cos(A+B)

Answer 2

cos(A)cos(B) - sin(A)sin(B)

Question 3

cos(A-B)

Answer 3

cos(A)cos(B) + sin(A)sin(B)

Question 4

tan(A+B)

Answer 4

[tan(A) + tan(B)]/[1 - tan(A)tan(B)]

Question 5

tan(A-B)

Answer 5

[tan(A) - tan(B)]/[1 + tan(A)tan(B)]

Question 6

tan(θ)

Answer 6

sin(θ)/cos(θ)

Question 7

cot(θ)

Answer 7

cos(θ)/sin(θ)

Question 8

sin²θ + cos²θ

Answer 8

1

Question 9

sec²θ - tan²θ

Answer 9

1

Question 10

csc²θ - cot²θ

Answer 10

1

Question 11

sin(-θ)

Answer 11

-sin(θ)

Question 12

tan(-θ)

Answer 12

-tan(θ)

Question 13

csc(-θ)

Answer 13

-csc(θ)

Question 14

cos(-θ)

Answer 14

cos(θ)

Question 15

cot(-θ)

Answer 15

-cot(θ)

Question 16

sec(-θ)

Answer 16

sec(θ)

Question 17

sin(π/2 - θ)

Answer 17

cos(θ) (and vice versa)

Question 18

tan(π/2 - θ)

Answer 18

cot(θ) (and vice versa)

Question 19

csc(π/2 - θ)

Answer 19

sec(θ) (and vice versa)

Question 20

sin(2θ)

Answer 20

2sin(θ)cos(θ)

Question 21

cos(2θ)

Answer 21

cos²θ - sin²θ or 2cos²θ -1 or 1 - 2sin²θ

Question 22

tan(2θ)

Answer 22

(2tanθ)/(1 - tan²θ)

Question 23

sin²θ

Answer 23

[1 - cos(2θ)]/2

Question 24

cos²θ

Answer 24

[1 + cos(2θ)]/2

Question 25

tan²θ

Answer 25

[1 - cos(2θ)]/[1 + cos(2θ)]

Question 26

sinA + sinB

Answer 26

2sin[(A+B)/2]cos[(A-B)/2]

Question 27

sinA - sinB

Answer 27

2cos[(A+B)/2]sin[(A-B)/2]

Question 28

cosA + cosB

Answer 28

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

Question 29

cosA - cosB

Answer 29

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

Question 30

sin(A)sin(B)

Answer 30

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

Question 31

cos(A)cos(B)

Answer 31

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

Question 32

sin(A)cos(B)

Answer 32

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

Question 33

cos(A)sin(B)

Answer 33

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