Studied by 4 peoplecos²(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))
Note
Flashcard