Trig Identities, Derivatives and Integrals

sinx/cosx

tan x

cosx/sinx

cot x

sin²x+cos²x

1

tan²x+1

sec²x

1+cot²x

csc²x

Integral of sin u dx

-cos u + C

Integral of cos u dx

sin u + C

Integral of sec²u dx

tan u + C

Integral of csc²u dx

-cot u + C

Integral of sec u tan u dx

sec u + C

Integral of csc u cot u dx

-csc u + C

Derivative of sin u

cos u du/dx

Derivative of cos u

-sin u du/dx

Derivative of tan u

sec²u du/dx

Derivative of cot u

-csc²u du/dx

Derivative of sec u

sec u tan u du/dx

Derivative of csc u

-csc u cot u du/dx

Derivative of ln u

u'/u

Derivative of ln |u|

u'/u

Integral of tan u du

-ln|cos u| + C

Integral of cot u du

ln|sin u| + C

Integral of sec u du

ln|sec u + tan u| + C

Integral of csc u du

-ln|csc u + cot u| + C

Derivative of e^u

e^u u'

Integral of e^u du

e^u + C

Derivative of a^u

(ln a)a^u u'

Derivative of log base a of u

u'/u ln a

Integral of a^u du

a^u/ln a + C

Derivative of (f^-1)(x)

1/f'(f^-1(x))

Integral of du/u

ln|u| + C

Derivative of arcsin u

u'/√1-u²

Derivative arccos u

-u'/√1-u²

Derivative of arctan u

u'/1+u²

Derivative of arccot u

-u'/1+u²

Derivative of arcsec u

u'/|u|√u²-1

Derivative of arccsc u

-u'/|u|√u²-1

Integral of du/√(a²-u²)

arcsin u/a + C

Integral of du/(a²+u²)

1/a arctan u/a + C

Integral of du/[u√(u²-a²)]

1/a arcsec |u|/a + C

sin (A+B)

sinAcosB+cosAsinB

sin (A-B)

sinAcosB-cosAsinB

cos (A+B)

cosAcosB-sinAsinB

cos (A-B)

cosAcosB+sinAsinB

tan (A+B)

(tanA+tanB)/(1-tanAtanB)

tan (A-B)

(tanA-tanB)/(1+tanAtanB)

sin2A

2sinAcosA

cos2A

cos²A +sin²A

cos2A

1-2sin²A

cos2A

2cos²A-1

sin²A

(1-cos2A)/2

cos²A

(1+cos2A)/2

tan²A

(1-cos2A)/(1+cos2A)

integral csc x cot x

-csc x