Trig Identities

sin²(x) + cos²(x)

1

1 + tan²(x)

sec²(x)

1 + cot²(x)

csc²(x)

sin(2x)

2 sin(x) cos(x)

cos(2x) (in terms of sin and cos)

cos²(x) - sin²(x)

cos(2x) (in terms of cos only)

2 cos²(x) - 1

cos(2x) (in terms of sin only)

1 - 2 sin²(x)

sin²(x) (Power-Reducing Identity)

(1 - cos(2x)) / 2

cos²(x) (Power-Reducing Identity)

(1 + cos(2x)) / 2

d/dx [sin(x)]

cos(x)

d/dx [cos(x)]

-sin(x)

d/dx [tan(x)]

sec²(x)

d/dx [csc(x)]

-csc(x) cot(x)

d/dx [sec(x)]

sec(x) tan(x)

d/dx [cot(x)]

-csc²(x)

∫ sin(x) dx

-cos(x) + C

∫ cos(x) dx

sin(x) + C

∫ sec²(x) dx

tan(x) + C

∫ csc²(x) dx

-cot(x) + C

∫ sec(x) tan(x) dx

sec(x) + C

∫ csc(x) cot(x) dx

-csc(x) + C

∫ tan(x) dx

ln|sec(x)| + C (or -ln|cos(x)| + C)

∫ sec(x) dx

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

d/dx [arcsin(x)]

1 / √(1 - x²)

d/dx [arctan(x)]

1 / (1 + x²)