trig identities

sin(-x)

-sin(x)

cos(x)

cos(-x)

sin(a+b)

sinacosb+sinbcosa

sin(a-b)

sinacosb-cosasinb

cos(a+b)

cosacosb-sinasinb

cos(a-b)

cosacosb+sinasinb

sin2x

2sinxcosx

cos2x

• cos²x-sin²x

• 1-2sin²x

• 2cos²x-1

tan(a+b)

tana+tanb / 1-tanatanb

tan(a-b)

tana-tanb/1+tanatanb

tan2x

2tanx / 1-tan²x

1+cot²x

cosec²x

tan²x+1

sec²x

HA

m<n y=0

m>n no HA or oblique so long diviion

m=n y=a/b (the leading coefficients)

complex polar form

modulus(costheta+isintheta)

loga(x) = b

a^b = x

range of fx

domain of f'-1x

induction

base case

holds true n=1

assume the result holds true for n=k

then n=k+1

if the result holds true for n=k, then it is true for n=k+1. as it is true n=1, the result holds true for all n