BC calc powers of trig and trig sub

cos²x → identity

1 - sin²x

sin²x → identity

1 - cos²x

cos²x → power reducers

(1+cos2x)/2 = ½ + ½cos2x = ½(1+cos2x)

sin²x → power reducers

(1-cos2x)/2 = ½ - ½cos2x = ½(1-cos2x)

sec²x

1 + tan²x

tan²x

sec²x - 1

sin2θ

2sinθcosθ

cos2θ

cos²θ - sin²θ

sinAcosB

½[sin(A - B) + sin(A + B)]

sinAsinB

½[cos(A - B) - cos(A + B)]

cosAcosB

½[cos(A - B) + cos(A + B)]

sqrt (a² - x²)

x = asinθ

op →u , adj → sqrt , hyp → a

sqrt (a² + x²)

x = atanθ

op →u , adj → a , hyp → sqrt

sqrt (x² - a²)

x = asecθ

op → sqrt , adj → a , hyp → u

int of secx dx

ln|tanx + secx| + C

int of sinx dx

-cosx + C

int of tanx dx

ln|secx| + C

int of csc dx

ln|cscx - cotx| + C = ln|tan(x/2)| + C

int of cosx dx

sinx + C

int of cotx dx

ln|sinx| + C

int of sec²x dx

tanx + C

int of csc²x dx

-cotx + C