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reciprocal of sin x
1/csc x

reciprocal of cos x
1/sec x

reciprocal of tan x
1/cot x

reciprocal of csc x
1/sin x

reciprocal of sec x
1/cos x

reciprocal of cot x
1/tan x

pythagorean identities
 sin^{2}x + cos^{2}x = 1
 1 + tan^{2}x = sec^{2}x
 1 = cot^{2}x = csc^{2}x

quotient identity
 tan x = sin x/cos x
 cot x = cos x/sin x

sumdifference formulas
 sin (x +/ u) = sin x cos u +/ cos x sin u
 cos (x +/ u) = cos x cos u /+ sin x sin u
 tan (x +/ u) = (tan x +/ tan u)/(1 /+ tan x tan u)

double angle formulas
 sin(2x) = 2sin x cos x
 cos(2x) = cos^{2}x  sin^{2}x = 2cos^{2}x  1 = 1  2sin^{2}x
 tan(2x) = (2tan x) /(1  tan^{2} x)

