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Pythagorean Identity sin cos
sin²x + cos²x = 1
Pythagorean Identity tan sec
1 + tan²x = sec²x
Pythagorean Identity cot csc
1 + cot²x = csc²x
Reciprocal Identity of sin
sin x = 1/csc x
Reciprocal Identity of cos
cos x = 1/sec x
Reciprocal Identity of tan
tan x = 1/cot x
Reciprocal Identity of csc
csc x = 1/sin x
Reciprocal Identity of sec
sec x = 1/cos x
Reciprocal Identity of cot
cot x = 1/tan x
Even-Odd Identity sin
sin(-x) = -sin x
Even-Odd Identity cos
cos(-x) = cos x
Even-Odd Identity tan
tan(-x) = -tan x
Even-Odd Identity sec
sec(-x) = sec x
Even-Odd Identity cot
cot(-x) = -cot x
Even-Odd Identity csc
csc(-x) = -csc x
Double-Angle Identity for sin
sin 2x = 2sin x cos x
Double-Angle Identity for cos
cos 2x = 1 - 2sin²x
Double-Angle Identity for tan
tan 2x = 2tan x / (1 - tan²x)
Derivative of sin
d/dx sin x = cos x
Derivative of cos
d/dx cos x = -sin x
Derivative of tan
d/dx tan x = sec²x
Derivative of cot
d/dx cot x = -csc²x
Derivative of sec
d/dx sec x = sec x tan x
Derivative of csc
d/dx csc x = -csc x cot x
Integral of sin
∫ sin x dx = -cos x + C
Integral of cos
∫ cos x dx = sin x + C
Integral of tan
∫ tan x dx = ln(sec x) + C
Integral of cot
∫ cot x dx = ln(sin x) + C
Integral of sec
∫ sec x dx = ln(sec x + tan x) + C
Integral of csc
∫ csc x dx = ln(csc x - cot x) + C
Power Reducing Identity for sin
sin²x = (1 - cos 2x)/2
Power Reducing Identity for cos
cos²x = (1 + cos 2x)/2
Power Reducing Identity for tan
tan²x = (1 - cos 2x)/(1 + cos 2x)
Tangent Identity
tan x = sin x / cos x
Cotangent Identity
cot x = cos x / sin x