Trig identities

Question 1

Trig identities

Answer 1

• sin^20 + cos^20 = 1
• tanx = sinx/cosx
• cosec^2x = 1 + cot^2x
• 1 + tan^2x = sec^2x
• cotx = cosx/ sinx

Question 2

Sin reciprocal

Answer 2

Cosec (x)

Question 3

Cos reciprocal

Answer 3

Sec(x)

Question 4

Tan reciprocal

Answer 4

Cot (x)

Question 5

Domain and range of the sec graph

Answer 5

Domain- x ≠ nπ /2

Range- sec(x) > or = 1
Sec (x) < or = -1

Question 6

Domain and range of cosec graph

Answer 6

Domain- x≠ nπ

Range- Cosec > or = 1
Cosec < or = -1

Question 7

Domain and range of cot graph

Answer 7

Domain- x≠ nπ For even values of n

Range- cot (x) real numbers

Question 8

Domain and range of tan graph

Answer 8

Domain- x≠ nπ /2 for odd values of n

Range- real numbers

Question 9

Cos(A+B) compound angle formula

Answer 9

CosACosB - SinASinB

Question 10

Cos(A-B) compound angle formula

Answer 10

CosACosB + SinASinB

Question 11

Sin(A+B) compound angle formula

Answer 11

SinACosB + CosASinB

Question 12

Sin(A-B) compound angle formula

Answer 12

SinACosB - CosASinB

Question 13

Tan(A+B) compound angle formula

Answer 13

(tanA + tanB) / (1-tanAtanB)

Question 14

Tan(A-B) compound angle formula

Answer 14

(tanA - tanB) / (1+tanAtanB)

Question 15

sin 2Θ double angle formula

Answer 15

2SinΘCosΘ

Question 16

Cos2Θ double angle formula

Answer 16

cos^2Θ - sin^Θ
1-2Sin^2Θ
2Cos^2Θ - 1

Question 17

tan2Θ double angle formula

Answer 17

(2tanΘ / 1-tan^2Θ)

Question 18

Sin^2Θ half angle formula

Answer 18

1-Cos2Θ /2

Question 19

Sin (x/2) half angle formula

Answer 19

square root of +-

1-cosx /2

Question 20

Cos^2Θ half angle formula

Answer 20

1 + cos2Θ /2

Question 21

Cos(x/2) half angle formula

Answer 21

square root of +-

1+Cosx /2

Question 22

Tan(x/2) half angle formula

Answer 22

Square root of +-

1-cos(x))/(1+cos(x)