Trigonometry

Question 1

sin(−θ)

Answer 1

−sin θ

Question 2

cos2A

Answer 2

cos²A–sin²A = 1–2sin2A = 2cos²A-1 = [(1-tan²A)/(1+tan²A)]

Question 3

sin x – sin y

Answer 3

2 cos [(x+y)/2] sin [(x-y)/2]

Question 4

cos(π/2-A)

Answer 4

sin A

Question 5

sin(2π-A)

Answer 5

-sin A

Question 6

sin(2π-A)

Answer 6

-sin A

Question 7

sin x + sin y

Answer 7

= 2 sin [(x+y)/2] cos [(x-y)/2]

Question 8

sin(π+A)

Answer 8

-sin A

Question 9

cot(A-B)

Answer 9

= [(cot A cot B + 1)/(cot B – cot A)]

Question 10

cos3A =

Answer 10

4cos³A – 3cosA

Question 11

sin3A =

Answer 11

3sinA – 4sin³A

Question 12

sin2A

Answer 12

2sinAcosA = [2tan A /(1+tan²A)]

Question 13

cos x – cos y

Answer 13

-2 sin [(x+y)/2] sin [(x-y)/2]

Question 14

tan 2A

Answer 14

(2 tan A)/(1-tan²A)

Question 15

cos(−θ)

Answer 15

cos θ

Question 16

cos(A+B)

Answer 16

cosAcosB - sinAsinB

Question 17

2cosAsinB

Answer 17

sin(A+B) - sin(A-B)

Question 18

tan(−θ)

Answer 18

−tan θ

Question 19

cot(A+B)

Answer 19

[(cot A cot B − 1)/(cot B + cot A)]

Question 20

sin(π/2-A)

Answer 20

cos A

Question 21

tan3A =

Answer 21

[3tanA–tan³A]/[1−3tan²A]

Question 22

cos(π-A)

Answer 22

-cos A

Question 23

cos(A-B)

Answer 23

cosAcosB + sinAsinB

Question 24

tan(A-B)

Answer 24

[(tan A – tan B)/(1 + tan A tan B)]

Question 25

2sinAcosB

Answer 25

sin(A+B) + sin(A-B)

Question 26

tan(A+B) =

Answer 26

[(tan A + tan B)/(1 – tan A tan B)]

Question 27

cos(2π-A)

Answer 27

= cos A

Question 28

sin(π-A)

Answer 28

sin A

Question 29

-2sinAsinB

Answer 29

cos(A+B) - cos(A-B)

Question 30

2sinAsinB

Answer 30

cos(A-B) - cos(A+B)

Question 31

cos x + cos y

Answer 31

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

Question 32

cosec(−θ)

Answer 32

−cosecθ