Trigonometry

Question 1

sin^2θ + cos^2θ

Answer 1

1

Question 2

1 + tan^2θ

Answer 2

sec^2θ

Question 3

1+cot^2θ

Answer 3

cosec^2θ

Question 4

sin^4θ + cos^4θ

Answer 4

1-2sin^2θcos^2θ

Question 5

sin^6θ + cos^6θ

Answer 5

1-3sin^2θcos^2θ

Question 6

sin(A+B)

Answer 6

sinAcosB+cosAsinB

Question 7

sin(A-B)

Answer 7

sinAcosB-cosAsinB

Question 8

cos(A+B)

Answer 8

cosAcosB-sinAsinB

Question 9

cos(A-B)

Answer 9

cosAcosB+sinAsinB

Question 10

tan(A+B)

Answer 10

(tanA+tanB)/1-tanAtanB

Question 11

tan(A-B)

Answer 11

(tanA-tanB)/1+tanAtanB

Question 12

cot(A+B)

Answer 12

cotAcotB-1/cotA+cotB

Question 13

cot(A-B)

Answer 13

cotAcotB+1/cotA-cotB

Question 14

2sinAcosB

Answer 14

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

Question 15

2cosAsinB

Answer 15

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

Question 16

2cosAcosB

Answer 16

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

Question 17

2sinAsinB

Answer 17

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

Question 18

sin2θ

Answer 18

2sinθcosθ

Question 19

cos2θ

Answer 19

2cos^2θ-1
or
1-2sin^2θ

Question 20

tan2θ

Answer 20

2tanθ/1-tan^2θ

Question 21

sin3θ

Answer 21

3sinθ-4sin^3θ

Question 22

cos3θ

Answer 22

4cos^3θ-3cosθ

Question 23

tan3θ

Answer 23

3tanθ-tan^3θ/1 - 3tan^2θ

Question 24

sinθsin(60-θ)sin(60+θ)

Answer 24

sin3θ/4

Question 25

cosθcos(60-θ)cos(60+θ)

Answer 25

cos3θ/4

Question 26

tanθtan(60-θ)tan(60+θ)

Answer 26

tan3θ

Question 27

cotθcot(60-θ)cot(60+θ)

Answer 27

cot3θ

Question 28

tanθ+tan(60+θ)+tan(60-θ)

Answer 28

3tan3θ

Question 29

Range of sin and cos function

Answer 29

[-1,1]

Question 30

Range of cot and tan function

Answer 30

(-∞, ∞)

Question 31

Range of sec and cosec function

Answer 31

(-∞, -1]∪[1, ∞)

Question 32

General Form of Angle of any sin function

Answer 32

x = nπ + (-1)^nα, where n belongs to integer

Question 33

General Form of Angle of any cos function

Answer 33

x = 2nπ±α, where n belongs to integer

Question 34

General Form of Angle of any tan function

Answer 34

x = nπ+α, where n belongs to integer

Question 35

General Form of Angle of any sin^2, cos^2 and tan^2 function

Answer 35

x = nπ±α, where n belongs to integer

Question 36

Principal Solution

Answer 36

Solution of trigonometric equation lying in the interval [0, 2π)

Question 37

General Solution

Answer 37

Solutions represented using a general formula

Question 38

Particular Solution

Answer 38

Solutions of trigonometric equations lying in the particular interval