Trig Ident

Question 1

sin(90°−x)

Answer 1

cos x

Question 2

cos(90°−x)

Answer 2

sin x

Question 3

tan(90°−x)

Answer 3

cot x

Question 4

cot(90°−x)

Answer 4

tan x

Question 5

sec(90°−x)

Answer 5

cosec x

Question 6

cosec(90°−x)

Answer 6

sec x

Question 7

sin(x+y)

Answer 7

sin(x)cos(y) + cos(x)sin(y)

Question 8

sin(x-y)

Answer 8

sin(x)cos(y) – cos(x)sin(y)

Question 9

cos(x+y)

Answer 9

cos(x)cos(y) – sin(x)sin(y)

Question 10

cos(x-y)

Answer 10

cos(x)cos(y) + sin(x)sin(y

Question 11

tan (x+y)

Answer 11

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

Question 12

tan (x-y)

Answer 12

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

Question 13

sin (2x)

Answer 13

2sin(x) * cos(x) = [2tan x/(1 + tan^2(x)]

Question 14

cos (2x)

Answer 14

cos^2(x) – sin^2(x) = [(1 – tan^2 (x)/(1 + tan^2(x)] = 2cos^2(x) – 1 = 1 – 2sin^2(x)

Question 15

tan (2x)

Answer 15

[2tan(x)]/ [1 – tan^2(x)]

Question 16

sec (2x)

Answer 16

sec^2(x)/(2 – sec^2(x))

Question 17

cosec (2x)

Answer 17

(sec x * cosec x)/2

Question 18

sin^-1 (–x)

Answer 18

– sin^-1 x

Question 19

cos^-1 (–x)

Answer 19

π – cos^-1 x

Question 20

tan^-1 (–x)

Answer 20

– tan^-1 x

Question 21

cosec^-1 (–x)

Answer 21

– cosec^-1 x

Question 22

sec^-1 (–x)

Answer 22

π – sec^-1 x

Question 23

cot^-1 (–x)

Answer 23

π – cot^-1 x

Question 24

sin 3x

Answer 24

3sin x – 4sin^3(x)

Question 25

cos 3x

Answer 25

4cos^3 x – 3cos^3(x)

Question 26

tan 3x

Answer 26

3tanx - tan^3(x) / 1-tan^2(x)

Question 27

sinx + siny

Answer 27

2[sin((x + y)/2)cos((x − y)/2)]

Question 28

sinx − siny

Answer 28

2[cos((x + y)/2)sin((x − y)/2)]

Question 29

cosx + cosy

Answer 29

2[cos((x + y)/2)cos((x − y)/2)]

Question 30

cosx − cosy

Answer 30

−2[sin((x + y)/2)sin((x − y)/2)]

Question 31

sinx⋅cosy

Answer 31

[sin(x + y) + sin(x − y)]/2

Question 32

cosx⋅cosy

Answer 32

[cos(x + y) + cos(x − y)]/2

Question 33

sinx⋅siny

Answer 33

[cos(x − y) − cos(x + y)]/2