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Maths > Trigonometry > Flashcards

Trigonometry Flashcards

1
Q
  1. Sin(A+B)
A

SinA cosB + cosA sinB

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2
Q
  1. Cos(A+B)
A

CosA cosB - sinA sinB

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3
Q
  1. Tan(A+B)
A

tanA + tanB / 1- tanA tanB

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4
Q

sin(A-B)

A

sinA cosB- cosA sinB

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5
Q

Cos(A- B)

A

cosA cosB + sinA sinB

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6
Q

tan(A-B)

A

tanA - tanB / 1+ tanA tanB

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7
Q

cot(A+B)

A

cotA cotB -1 / cotA+ cotB

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8
Q

cot(A-B)

A

cotA cotB + 1 / cotB - cotA

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9
Q

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

A

sin²A - sin²B ;
cos²B - cos²A

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10
Q

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

A

Cos²A - sin²B ;
Cos²B - sin²A

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11
Q

Sin2A

A

2sinA cosA ;
2tanA / 1+ tan²A

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12
Q

Cos2A

A

Cos²A - sin²A ;
1- tan²A / 1+ tan²A

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13
Q

1 + cos2A

A

2 cos²A

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14
Q

1 - cos2A

A

2 sin²A

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15
Q

tan2A

A

2 tanA / 1- tan²A

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16
Q

Sin3A

A

3 sinA - 4 sin³A

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17
Q

Cos3A

A

4cos³A - 3 cosA

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18
Q

tan3A

A

3 tanA - tan³A / 1 - 3 tan²A

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19
Q

2 sinA cosB

A

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

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20
Q

2 cosA sinB

A

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

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21
Q

2 cosA cosB

A

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

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22
Q

2 sinA sinB

A

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

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23
Q

SinC + sinD

A

2 sin (C+D/2) • cos (C-D/2)

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24
Q

Sin C - sinD

A

2 cos (C+D/2) • Sin (C-D/2)

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25
Q

CosC + cosD

A

2 cos (C+D/2) • cos (C-D/2)

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26
Q

Cos C - cos D

A

-[ 2 sin( C+D/2) • sin (C-D/2) ]

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27
Q

1 - cosA / sinA ;
SinA / 1 + cosA

A

tan A/2

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28
Q

1+ cosA /sinA

A

Cot A/2

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29
Q

1- cosA / 1+ cosA

A

tan² A/2

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30
Q

1+ cosA / 1- cosA

A

Cot² A/2

31
Q

tan( π/ 4 + A )

A

1+tanA / 1- tanA ;
1 + sin2A / cos2A ;
CosA + sinA / cosA - sinA

32
Q

tan( π/4- A )

A

1-tanA /1+ tanA ;
1- sin2A / cos2A ;
CosA - sinA / cosA + sinA

33
Q

SinA sin( 60°+A ) sin( 60°-A )

A

1/4 sin3A

34
Q

CosA cos( 60°+A ) cos( 60°-A )

A

1/4 cos3A

35
Q

tanA tan( 60°+A ) tan( 60°-A )

A

tan3A

36
Q

tanA + tanB

A

Sin( A+B ) / cosA cosB

37
Q

tanA - tanB

A

Sin (A- B) / cosA cosB

38
Q

CotA + cotB

A

Sin(B+A) / sinA sinB

39
Q

CotA - cotB

A

Sin(B-A)/ sinA sinB

40
Q

1+ tanA tanB

A

Cos( A-B ) / cosA cosB

41
Q

1- tanA tanB

A

Cos (A+B)/ cos A cosB

42
Q

1+ cotA cotB

A

Cos(A-B)/ sinA sinB

43
Q

1- cotA cotB

A

-[ Cos(A+B)/ sinA sinB ]

44
Q

1+ sin2A

A

(SinA + cosA)²

45
Q

1- sin2A

A

(SinA - cosA)²

46
Q

CotA - tanA

A

2 cot2A

47
Q

CotA + tanA

A

2 cosec2A

48
Q

√ 1+ sin2A = | sinA + cosA|
Why??

A

In trigno , whenever we remove square root of trignometric functions we must add modulus on it .

49
Q

Sin⁴ A + cos⁴ A

A

1 - 2 sin²A cos²A

50
Q

Sin⁶A + cos⁶A

A

1- 3 sin²A cos²A

51
Q

Degree to radian

A

1° = π/180

52
Q

Relation between arc and angle

A

l = Ar ;
Area = 1/2 Ar² ;
Area = 1/2 rl
Where A is angle

53
Q

Domain of sinx and cosx

A

Domain –> R

54
Q

Range of cosx and sinx

A

Range –> [ -1,1 ]

55
Q

Range sec x and cosec x

A

(- infinity, -1] U [1 , infinity)

56
Q

Range of tanx and cot x

A

(- infinity, infinity)

57
Q

Domain tan x and cot x

A

X€ R - { (2n+1)π/2 } ;
X€ R - { nπ }

58
Q

Domain of secx and cosecx

A

X€ R - { (2n+1)π/2 }
X€ R - { nπ }

59
Q

Range of (a sinx + b cosx )

A

[ -( √ a²+b² ) , ( √a²+ b² ) ]

60
Q

SinA + sin( A+B ) + sin ( A+2B )+………….+ Sin( A+ (n-1) B ) =

A

Angles must be in AP

[ Sin (n• B/2 ) / sin B/2 ] •
sin (A+ (n-1) B /2)

Common difference = B
First term= A

61
Q

CosA + cos( A+B ) + cos ( A+2B )+………….+ Cos( A+ (n-1) B ) =

A

Angles must be in AP

[ Sin (n• B/2 ) / sin B/2 ] •
Cos (A+ (n-1) B /2)

Common difference = B
First term= A

62
Q

Cosec x + cosec 2x + cosec 3x + ………..+ Cosec 2^n x =

A

angles must be in GP

Cot (x/2) - cot (2^n x )

63
Q

Cos A cos2A cos 4A cos 8A ……..cos (2^n-1)A =

A

series must be in gp and have 2 or 1/2 as common ratio

Sin( 2^n A )/ 2^n sin A

64
Q

Sin2A + sin2B + sin2C

A

4 sinA sinB sinC

65
Q

Cos2A + cos2B + cos2C

A
  • 1- 4 cosA cosB cosC
66
Q

SinA + sinB + sinC

A

4 cosA/2 cosB/2 cosC/2

67
Q

Cos A + cosB + cosC

A

1+4 sinA/2 sinB/2 sinC/2

68
Q

Cos²A + cos²B + cos²C

A

1- 2 cosA cosB cosC

69
Q

Sin²A + sin²B + sin²C

A

2 + 2 cosA cosB cosC

70
Q

Sin²A + sin²B - sin²C

A

2 sinA sinB cosC

71
Q

Cos²A/2 + cos²B/2 + cos²C/2

A

2+2 sinA/2 sinB/2 sinC/2

72
Q

tanA + tanB + tanC

A

tanA tanB tanC

73
Q

tanA/2 tanB/2 + tanB/2 tanC/2 + tanC/2 tanA/2

A

1

74
Q

CotA cotB + cotB cotC + cotC cotA

A

1

Maths (2 decks)

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