Trig Ident Flashcards
sin(90°−x)
cos x
cos(90°−x)
sin x
tan(90°−x)
cot x
cot(90°−x)
tan x
sec(90°−x)
cosec x
cosec(90°−x)
sec x
sin(x+y)
sin(x)cos(y) + cos(x)sin(y)
sin(x-y)
sin(x)cos(y) – cos(x)sin(y)
cos(x+y)
cos(x)cos(y) – sin(x)sin(y)
cos(x-y)
cos(x)cos(y) + sin(x)sin(y
tan (x+y)
tan(x)tan(y) / 1-tan(x)tan(y)
tan (x-y)
tan(x)tan(y) / 1+tan(x)tan(y)
sin (2x)
2sin(x) * cos(x) = [2tan x/(1 + tan^2(x)]
cos (2x)
cos^2(x) – sin^2(x) = [(1 – tan^2 (x)/(1 + tan^2(x)] = 2cos^2(x) – 1 = 1 – 2sin^2(x)
tan (2x)
[2tan(x)]/ [1 – tan^2(x)]
sec (2x)
sec^2(x)/(2 – sec^2(x))
cosec (2x)
(sec x * cosec x)/2
sin^-1 (–x)
– sin^-1 x
cos^-1 (–x)
π – cos^-1 x
tan^-1 (–x)
– tan^-1 x
cosec^-1 (–x)
– cosec^-1 x
sec^-1 (–x)
π – sec^-1 x
cot^-1 (–x)
π – cot^-1 x
sin 3x
3sin x – 4sin^3(x)
cos 3x
4cos^3 x – 3cos^3(x)
tan 3x
3tanx - tan^3(x) / 1-tan^2(x)
sinx + siny
2[sin((x + y)/2)cos((x − y)/2)]
sinx − siny
2[cos((x + y)/2)sin((x − y)/2)]
cosx + cosy
2[cos((x + y)/2)cos((x − y)/2)]
cosx − cosy
−2[sin((x + y)/2)sin((x − y)/2)]
sinx⋅cosy
[sin(x + y) + sin(x − y)]/2
cosx⋅cosy
[cos(x + y) + cos(x − y)]/2
sinx⋅siny
[cos(x − y) − cos(x + y)]/2
