Pre-calc Trig identities

cos²x+sin²x =

1

sec²x - tan²x =

1

1+tan²x =

sec²x

1 - sin²x =

cos²x

cot²x + 1 =

csc²

csc²x - cot²x =

1

sin/csc/tan/cot (-x) =

-sin/-csc/-tan/-cot (x)

cos/sec (-x) =

cos/sec (x)

for any Trig function (pi/2 - x):

sin goes to:

tan goes to:

sec goes to:

cos

cot

csc

when proving an identity, start with

the more complicated side and work towards the less complicated

when stuck, convert every term to:

terms that only contain cos and sin (like cos/sin for cot or 1/cos for sec)

sin(u+v) =

sin(u)cos(v) + cos(u)sin(v)

sin(u-v) =

sin(u)cos(v) - cos(u)sin(v)

cos(u+v)=

cos(u)cos(v) - sin(u)sin(v)

cos(u-v)

cos(u)cos(v) + sin(u)sin(v)

sin2(u) =

2sin(u)cos(u)

(1st answer) cos2(u) =

cos²(u) - sin²(u)

(2nd answer) cos2(u) =

2cos²(u) - 1

(3rd answer) cos2(u) =

1 - 2sin²(u)

tan2(u) =

2tan(u) / 1 - tan²(u)

tan(u+v) =

tan(u) + tan(v) / 1 - tan(u)tan(v)

tan(u-v) =

tan(u) - tan(v) / 1 + tan(u)tan(v)

cos(x)/sin(x) =

cot(x)

1/cot(x) =

tan(x)

1/sec(x) =

cos(x)

1/csc(x) =

sin(x)