TRIGONOMETRIC IDENTITIES

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