Can u send me all formulas of tringinometry..
Answers
Answer:
Sin A = Perpendicular/Hypotenuse
Cos A = Base/Hypotenuse
Tan A = Perpendicular/Base
Answer:
Basic formulas
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
Step-by-step explanation:
reciprocal
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot
sin(90°−x) = cos x
cos(90°−x) = sin x
tan(90°−x) = cot x
cot(90°−x) = tan x
sec(90°−x) = csc x
csc(90°−x) = sec x
Sum & Difference Identities
sin(x+y) = sin(x)cos(y)+cos(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)
sin(x–y) = sin(x)cos(y)–cos(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)
Double Angle Identities
sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]
cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
tan(2x) = [2tan(x)]/ [1−tan2(x)]
sec (2x) = sec2 x/(2-sec2 x)
csc (2x) = (sec x. csc x)/2
Triple Angle Identities
Sin 3x = 3sin x – 4sin3x
Cos 3x = 4cos3x-3cos x
Tan 3x = [3tanx-tan3x]/[1-3tan2x]
Half Angle Identities
sinx2=±1−cosx2−−−−−−√
cosx2=±1+cosx2−−−−−−√
tan(x2)=1−cos(x)1+cos(x)−−−−−−√
Also, tan(x2)=1−cos(x)1+cos(x)−−−−−−√=(1−cos(x))(1−cos(x))(1+cos(x))(1−cos(x))−−−−−−−−−−−−−√=(1−cos(x))21−cos2(x)−−−−−−−−√=(1−cos(x))2sin2(x)−−−−−−−−√=1−cos(x)sin(x) So, tan(x2)=1−cos(x)sin(x)
Product identities
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
Sum to Product Identities
sinx+siny=2sinx+y2cosx−y2
sinx−siny=2cosx+y2sinx−y2
cosx+cosy=2cosx+y2cosx−y2
cosx−cosy=−2sinx+y2sinx−y2
Inverse Trigonometry Formulas
sin-1 (–x) = – sin-1 x
cos-1 (–x) = π – sin-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