Trig Ident Flashcards
1
Q
sin(90°−x)
A
cos x
2
Q
cos(90°−x)
A
sin x
3
Q
tan(90°−x)
A
cot x
4
Q
cot(90°−x)
A
tan x
5
Q
sec(90°−x)
A
cosec x
6
Q
cosec(90°−x)
A
sec x
7
Q
sin(x+y)
A
sin(x)cos(y) + cos(x)sin(y)
8
Q
sin(x-y)
A
sin(x)cos(y) – cos(x)sin(y)
9
Q
cos(x+y)
A
cos(x)cos(y) – sin(x)sin(y)
10
Q
cos(x-y)
A
cos(x)cos(y) + sin(x)sin(y
11
Q
tan (x+y)
A
tan(x)tan(y) / 1-tan(x)tan(y)
12
Q
tan (x-y)
A
tan(x)tan(y) / 1+tan(x)tan(y)
13
Q
sin (2x)
A
2sin(x) * cos(x) = [2tan x/(1 + tan^2(x)]
14
Q
cos (2x)
A
cos^2(x) – sin^2(x) = [(1 – tan^2 (x)/(1 + tan^2(x)] = 2cos^2(x) – 1 = 1 – 2sin^2(x)
15
Q
tan (2x)
A
[2tan(x)]/ [1 – tan^2(x)]
16
Q
sec (2x)
A
sec^2(x)/(2 – sec^2(x))
17
Q
cosec (2x)
A
(sec x * cosec x)/2
18
Q
sin^-1 (–x)
A
– sin^-1 x
19
Q
cos^-1 (–x)
A
π – cos^-1 x
20
Q
tan^-1 (–x)
A
– tan^-1 x
21
Q
cosec^-1 (–x)
A
– cosec^-1 x
22
Q
sec^-1 (–x)
A
π – sec^-1 x
23
Q
cot^-1 (–x)
A
π – cot^-1 x
24
Q
sin 3x
A
3sin x – 4sin^3(x)
25
cos 3x
4cos^3 x – 3cos^3(x)
26
tan 3x
3tanx - tan^3(x) / 1-tan^2(x)
27
sinx + siny
2[sin((x + y)/2)cos((x − y)/2)]
28
sinx − siny
2[cos((x + y)/2)sin((x − y)/2)]
29
cosx + cosy
2[cos((x + y)/2)cos((x − y)/2)]
30
cosx − cosy
−2[sin((x + y)/2)sin((x − y)/2)]
31
sinx⋅cosy
[sin(x + y) + sin(x − y)]/2
32
cosx⋅cosy
[cos(x + y) + cos(x − y)]/2
33
sinx⋅siny
[cos(x − y) − cos(x + y)]/2
