Trigonometry Flashcards
1
Q
- Sin(A+B)
A
SinA cosB + cosA sinB
2
Q
- Cos(A+B)
A
CosA cosB - sinA sinB
3
Q
- Tan(A+B)
A
tanA + tanB / 1- tanA tanB
4
Q
sin(A-B)
A
sinA cosB- cosA sinB
5
Q
Cos(A- B)
A
cosA cosB + sinA sinB
6
Q
tan(A-B)
A
tanA - tanB / 1+ tanA tanB
7
Q
cot(A+B)
A
cotA cotB -1 / cotA+ cotB
8
Q
cot(A-B)
A
cotA cotB + 1 / cotB - cotA
9
Q
sin(A+B ) sin( A-B )
A
sin²A - sin²B ;
cos²B - cos²A
10
Q
Cos(A+B) cos (A-B)
A
Cos²A - sin²B ;
Cos²B - sin²A
11
Q
Sin2A
A
2sinA cosA ;
2tanA / 1+ tan²A
12
Q
Cos2A
A
Cos²A - sin²A ;
1- tan²A / 1+ tan²A
13
Q
1 + cos2A
A
2 cos²A
14
Q
1 - cos2A
A
2 sin²A
15
Q
tan2A
A
2 tanA / 1- tan²A
16
Q
Sin3A
A
3 sinA - 4 sin³A
17
Q
Cos3A
A
4cos³A - 3 cosA
18
Q
tan3A
A
3 tanA - tan³A / 1 - 3 tan²A
19
Q
2 sinA cosB
A
Sin( A+B ) + sin(A- B)
20
Q
2 cosA sinB
A
Sin (A+B) - sin(A-B)
21
Q
2 cosA cosB
A
Cos(A+B) + cos(A-B)
22
Q
2 sinA sinB
A
-[ cos(A+B) - cos (A-B) ]
23
Q
SinC + sinD
A
2 sin (C+D/2) • cos (C-D/2)
24
Q
Sin C - sinD
A
2 cos (C+D/2) • Sin (C-D/2)
25
CosC + cosD
2 cos (C+D/2) • cos (C-D/2)
26
Cos C - cos D
-[ 2 sin( C+D/2) • sin (C-D/2) ]
27
1 - cosA / sinA ;
SinA / 1 + cosA
tan A/2
28
1+ cosA /sinA
Cot A/2
29
1- cosA / 1+ cosA
tan² A/2
30
1+ cosA / 1- cosA
Cot² A/2
31
tan( π/ 4 + A )
1+tanA / 1- tanA ;
1 + sin2A / cos2A ;
CosA + sinA / cosA - sinA
32
tan( π/4- A )
1-tanA /1+ tanA ;
1- sin2A / cos2A ;
CosA - sinA / cosA + sinA
33
SinA sin( 60°+A ) sin( 60°-A )
1/4 sin3A
34
CosA cos( 60°+A ) cos( 60°-A )
1/4 cos3A
35
tanA tan( 60°+A ) tan( 60°-A )
tan3A
36
tanA + tanB
Sin( A+B ) / cosA cosB
37
tanA - tanB
Sin (A- B) / cosA cosB
38
CotA + cotB
Sin(B+A) / sinA sinB
39
CotA - cotB
Sin(B-A)/ sinA sinB
40
1+ tanA tanB
Cos( A-B ) / cosA cosB
41
1- tanA tanB
Cos (A+B)/ cos A cosB
42
1+ cotA cotB
Cos(A-B)/ sinA sinB
43
1- cotA cotB
-[ Cos(A+B)/ sinA sinB ]
44
1+ sin2A
(SinA + cosA)²
45
1- sin2A
(SinA - cosA)²
46
CotA - tanA
2 cot2A
47
CotA + tanA
2 cosec2A
48
√ 1+ sin2A = | sinA + cosA|
Why??
In trigno , whenever we remove square root of trignometric functions we must add modulus on it .
49
Sin⁴ A + cos⁴ A
1 - 2 sin²A cos²A
50
Sin⁶A + cos⁶A
1- 3 sin²A cos²A
51
Degree to radian
1° = π/180
52
Relation between arc and angle
l = Ar ;
Area = 1/2 Ar² ;
Area = 1/2 rl
Where A is angle
53
Domain of sinx and cosx
Domain --> R
54
Range of cosx and sinx
Range --> [ -1,1 ]
55
Range sec x and cosec x
(- infinity, -1] U [1 , infinity)
56
Range of tanx and cot x
(- infinity, infinity)
57
Domain tan x and cot x
X€ R - { (2n+1)π/2 } ;
X€ R - { nπ }
58
Domain of secx and cosecx
X€ R - { (2n+1)π/2 }
X€ R - { nπ }
59
Range of (a sinx + b cosx )
[ -( √ a²+b² ) , ( √a²+ b² ) ]
60
SinA + sin( A+B ) + sin ( A+2B )+.............+ Sin( A+ (n-1) B ) =
[ Sin (n• B/2 ) / sin B/2 ] •
sin (A+ (n-1) B /2)
# Angles must be in AP
Common difference = B
First term= A
61
CosA + cos( A+B ) + cos ( A+2B )+.............+ Cos( A+ (n-1) B ) =
[ Sin (n• B/2 ) / sin B/2 ] •
Cos (A+ (n-1) B /2)
# Angles must be in AP
Common difference = B
First term= A
62
Cosec x + cosec 2x + cosec 3x + ...........+ Cosec 2^n x =
Cot (x/2) - cot (2^n x )
#angles must be in GP
63
Cos A cos2A cos 4A cos 8A ........cos (2^n-1)A =
Sin( 2^n A )/ 2^n sin A
# series must be in gp and have 2 or 1/2 as common ratio
64
Sin2A + sin2B + sin2C
4 sinA sinB sinC
65
Cos2A + cos2B + cos2C
- 1- 4 cosA cosB cosC
66
SinA + sinB + sinC
4 cosA/2 cosB/2 cosC/2
67
Cos A + cosB + cosC
1+4 sinA/2 sinB/2 sinC/2
68
Cos²A + cos²B + cos²C
1- 2 cosA cosB cosC
69
Sin²A + sin²B + sin²C
2 + 2 cosA cosB cosC
70
Sin²A + sin²B - sin²C
2 sinA sinB cosC
71
Cos²A/2 + cos²B/2 + cos²C/2
2+2 sinA/2 sinB/2 sinC/2
72
tanA + tanB + tanC
tanA tanB tanC
73
tanA/2 tanB/2 + tanB/2 tanC/2 + tanC/2 tanA/2
1
74
CotA cotB + cotB cotC + cotC cotA
1
