Trig Integrals, Derivatives, and Identities

cos²(x) + sin²(x) =

1

1+tan²(x) =

sec²(x)

1+cot²(x) =

csc²(x)

sin(2x) =

2sin(x)cos(x)

cos(2x)=

cos²(x) - sin²(x)

cos(2x)=

1 - 2sin²(x)

cos(2x)=

2cos²(x)-1

cos²(x)=

(1+cos(2x))/2

sin²(x)=

(1-cos(2x))/2

∫tan(x)dx =

-ln|cos(x)| + C

∫tan(x)dx =

ln|sec(x)| + C

∫cot(x)dx =

ln|sin(x)| + C

∫cot(x)dx =

-ln|csc(x)| + C

∫sec(x)dx

ln|sec(x) + tan(x)| + C

∫csc(x)dx

-ln|csc(x) + cot(x)| + C

∫sec²(x)dx =

tan(x)

∫sec(x)tan(x)dx =

sec(x) + C

∫-csc²(x)dx =

cot(x) + C

∫-csc(x)cot(x)dx =

csc(x) + C

d/dx(tan(x)) =

sec²(x)

d/dx(sec(x)) =

sec(x)tan(x)

d/dx(cot(x)) =

-csc²(x)

d/dx(csc(x)) =

-csc(x)cot(x)

d/dx(-ln|cos(x)|) =

tan(x)

d/dx(ln|sec(x)|) =

tan(x)

d/dx(ln|sin(x)|) =

cot(x)

d/dx(-ln|csc(x)|) =

cot(x)

d/dx(ln|sec(x) + tan(x)|) =

sec(x)

d/dx(-ln|sec(x) + tan(x)|) =

csc(x)

d/dx(sin⁻¹(x)) =

1/√(1-x²)

d/dx(cos⁻¹(x)) =

-1/√(1-x²)

d/dx(tan⁻¹(x)) =

1/(1+x²)

d/dx(cot⁻¹(x)) =

-1/(1+x²)

d/dx(sec⁻¹(x)) =

1/(x√(x²-1))

d/dx(csc⁻¹(x)) =

-1/(x√(x²-1))