trig functions + trig sub

Pythagorean identity

sin²(x)+cos²(x)=1

double angle of sin

sin(2x) = 2sin(x)cos(x)

double angle of cos

cos(2x) = cos²(x)-sin²(x)

power reduction of cos

cos²(x) = ½ + cos(2x)/2

power reduction of sin

sin²(x) = ½ - cos(2x)/2

TOES identity

1 + tan²x = sec²x

COEC identity

1 + cot²x = csc²x

integral of tan(x)

x²+a²

let x = a tanθ

dx = a sec²θ dθ

tan²θ +1 = sec²θ

a²-x²

let x = a sinθ

dx = a cosθ dθ

1-sin²θ = cos²θ

x²-a²

let x = asecθ

dx = a secθ tanθ dθ

sec²θ - 1 = tan²θ