1 Sec X Cos X

Trigonometric Identities

(Math | Trig | Identities)

sin(theta) = a / c	csc(theta) = i / sin(theta) = c / a
cos(theta) = b / c	sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b	cot(theta) = one/ tan(theta) = b / a

sin(-10) = -sin(x)
csc(-x) = -csc(x)
cos(-x) = cos(x)
sec(-x) = sec(x)
tan(-x) = -tan(x)
cot(-x) = -cot(x)

sin^{^two}(x) + cos^{^ii}(ten) = 1	tan^{^ii}(x) + 1 = sec^{^2}(x)	cot^{^2}(x) + i = csc^{^two}(x)
sin(x y) = sin ten cos y cos 10 sin y
cos(ten y) = cos ten cosy sin ten sin y

tan(x y) = (tan 10 tan y) / (1 tan x tan y)

sin(2x) = 2 sin x cos x

cos(2x) = cos^{^2}(ten) - sin^{^2}(ten) = 2 cos^{^2}(10) - 1 = one - two sin^{^two}(x)

tan(2x) = two tan(x) / (1 - tan^{^2}(x))

sin^{^2}(x) = 1/2 - ane/two cos(2x)

cos^{^2}(10) = 1/2 + ane/2 cos(2x)

sin x - sin y = two sin( (x - y)/ii ) cos( (x + y)/2 )

cos x - cos y = -2 sin( (x - y)/two ) sin( (x + y)/2 )

Trig Tabular array of Mutual Angles
angle	0	thirty	45	sixty	xc
sin^{^2}(a)	0/4	1/4	2/4	3/4	4/four
cos^{^two}(a)	4/four	three/four	2/4	i/4	0/four
tan^{^ii}(a)	0/4	1/3	2/two	3/1	4/0

Given Triangle abc, with angles A,B,C; a is reverse to A, b opposite B, c reverse C:

a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines)

c^{^2} = a^{^ii} + b^{^2} - 2ab cos(C)

b^{^2} = a^{^2} + c^{^2} - 2ac cos(B)

a^{^2} = b^{^2} + c^{^two} - 2bc cos(A)

(Police of Cosines)

(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/two] (Law of Tangents)

1 Sec X Cos X,

Source: http://www.math.com/tables/trig/identities.htm