Trigonemetric Identities Review

Basic Trig review for Calc II.

sin(a+b)

sin(a)cos(b)+cos(a)sin(b)

sin(a−b)

sin(a)cos(b)−cos(a)sin(b)

cos(a+b)

cos(a)cos(b)−sin(a)sin(b)

cos(a−b)

cos(a)cos(b)+sin(a)sin(b)

tan(a+b)

tan(a)+tan(b)​/(1−tan(a)tan(b))

tan(a-b)

tan(a)-tan(b)/(1+tan(a)tan(b))

sin(2a)

2sin(a)cos(a)

cos(2a)

cos²(a)−sin²(a)
2cos²(a)−1
1−2sin²(a)

tan(2a)

2tan(a)​/(1−tan²(a))

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec²x

d/dx cot(x)

-csc²(x)

d/dx sec(x)

sec(x)tan(x)

d/dx csc(x)

-csc(x)cot(x)

∫sin⁡(x)dx

-cos(x)+C

∫cos(x)dx

sin(x)+C

∫tan(x)dx

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

∫cot(x)dx

ln|sin(x)|+C

∫sec(x)dx

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

∫csc(x)dx

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

∫arcsin(x)dx

=xarcsin(x)+√(1−x2​)+C

∫arccos(x)dx

xarccos(x)-√(1−x2​)+C

∫arctan(x)dx

xarctan(x)-1/2ln(1+x²)+C

∫arccot(x)dx

xarccot(x)+1/2 ​ln(1+x)²+C

∫arcsec(x)dx

xarcsec(x)−ln​|x+√x²−1|​​+C

∫arccsc(x)dx

xarccsc(x)+ln​|x+√x²−1|​​+C