Ap Precalc trig identities

Trig proofs using pythagorean(pyt), power reducing(pwr), Half angle, double angle, sum, and difference identities

tan(x/2)

±(1-cosx)/sinx

cos(x/2)

± square root of (1+cosx)/2

sin(x/2)

± sqare root of (1-cosx)/2

Cos(a+b)

CosaCosb-SinaSinb

sin(a+b)

SinaCosb+SinbCosa

Tan(2x)

(2tanx)/(1-tan²x)

tan(a-b)

(Tana-Tanb)/(1+TanaTanb)

cos(2x)

cos²x-sin²x

sin(2x)

2SinxCosx

Sec(a-b)

(SecaSecb)/(1+SecaSecb)

sin²x

pwr

(1-cos(2x))/2

Cos²x

pwr

1+cos(2x)/2

tan^2x

^pwr

1-cos(2x)/1+cos(2x)

Cot²x

pwr

1+cos(2x)/1-cos(2x)

Sec(a+b)

SecaSecb/1-SecaSecb

csc(x/2)

± square root of 2/1-cosx

cot(2x)

cot²x-1/2cotx

sec(2x)

1/cos²x-sin²x

csc(2x)

1/2sinxcosx

tan(a+b)

Tana+Tanb/1-TanaTanb

Tan²x

pyt

sec²x-1

cot²x

pyt

csc²x-1

sec²x

pyt

tan²x+1

cos²x

1-sin²x

cos(a-b)

CosaCosb-SinaSinb

Cot(a-b)

CotaCotb+1/Cota-Cotb

Cot(a+b)

CotaCotb-1/Cota+Cotb

csc(a-b)

CscaCscb/Csc²a-Csc²b

Csc(a+b)

CscaCscB/Csc²a-Csc²b

Cot(x/2)

sinx/1-cosx

sec(x/2)

± square root od 2/1+cosx

csc²x

^pwr

2/1-cos(2x)

sin²x

pyt

1-cos²x

Sec²x

pwr

2/1-cos(2x)

csc²x

pyt

1+cot