Trig Substitutions & Identities

d/dx (tan x)

sec²x

d/dx (sec x)

sec x tan x

d/dx (cot x)

-csc²x

d/dx (csc x)

-csc x cot x

sin²x + cos²x

1

tan²x + 1

sec²x

sin2x

2sin x cos x

cos2x

2 cos²x - 1

sqrt(a²-x²)

let x = a sin0

sqrt(x²-a²)

let x = a sec 0

sqrt(a²+x²)

let x = a tan 0

sin²0

½ (1-cos(20)

1-sin²x

cosx

1+tan²x

sec²x

1+cot²x

csc²x

1-sin²x

cos²x

sec²x-1

tan²x

csc²x-1

cot²x

1-cos²x

sin²x

sec²x-tan²x

1

csc²x-cot²x

1

d/dx(arctan)

1/1+x²