1. Trig Identities on the six trigonometric ratios:

(Note: trig is an abbreviation for trigonometric. We will use trig for the word trigonometric to avoid repetition and therefore boredom.)

1. Sinα = opposite side/hypotenuse = AB/AC

2. Cosα = adjacent side/hypotenuse = BC/AC

3. Tanα = opposite side/adjacent side = AB/BC

2. The reciprocal Trig identities   

1. cosecα = 1/sinα

2. secα = 1/cosα

3. cotα = 1/tanα

3. The three Pythagorean trig identities

1. Sin²α + Cos²α = 1

2. Sec²α – tan²α = 1,  Sec²α =  1+ tan²α

3. Cosec²α – cotan²α = 1, Cosec²α = 1+ cotan²α

4. The quotient Trig identities:

1. tan α = sin α /cos α

2. cot α = cos α /sin α

5. Trig identities of negative angles:

1. Sin (– α) = –sin α

2. cos (– α) = cos α

3. tan (– α) = – tanα

4. cot (– α) = – cotα

5. Sec (– α) = Sec α

6. cosec (– α) = – cosec α

6. Trig identities of compound angles

1. sin (A + B) = sinAcosB + cosAsinB

2. sin (A – B) = sinAcosB – cosAsinB

3. cos (A + B) = cosAcosB – sinAsinB

4. cos (A – B) = cosAcosB + sinAsinB

5. Tan(A + B) = (sinAcosB + cosAsinB)/(cosAcosB – sinAsinB)

6. Tan(A – B) = (sinAcosB – cosAsinB)/(cosAcosB + sinAsinB)

7. Trig identities on products of compound angles

1. sin(A + B)sin(A – B) = sin²A – sin²B Or cos²B – cos²A

2. cos (A + B)cos(A – B) = cos²A – sin²B Or cos²B – sin²A

3. tan (A + B)tan(A – B) = (tan²A – tan²B)/ (1 – tan²Atan²B)

4. tan(A + B + C) = (tan A + tan B + tan C – tanA tanB tanC)/ (1– tanAtanB – tanB tanC –tanC tanA)

8. Trig identities on conversion of sum of angles to product of angles

1. sin (A + B) + sin ( A – B) = 2sinAcosB

2. sin (A + B) – sin (A – B) = 2 cosAsinB

3. cos ( A + B ) + cos (A – B) = 2cosAcosB

4. cos ( A – B ) – cos (A + B) = 2sinAsinB

9. Trig identities on sums of angles.

10. trig identities on double angles:

1. Sin2A = 2sinAcosA Or 2tanA/ (1 + tan²A)

2. cos2A = 2cos²A – 1 Or 1 – 2sin²A Or (1 – tan²A)/(1 + tan²A)

3. tan2A = 2tanA/(1 – tan²A)

11. Trig identities on triple angles

1. Sin3A = 3sinA – 4sin³A

2. cos3A = 4cos³A – 3cosA

3. tan3A = (3tanA – tan³A)/(1 – 3tan²A)

12. Trig identities on sub-multiple angles

1. sin2A + sin2B + sin2C = 4sinAsinBsinC Or -1 – 4cosAcosBcosC

2. cos2A + cos2B + cos2C = 1 – 4 sinAsinBsinC

2. tan2A + tan2B + tan2C = tan2C tan2B tan2C

13. The law of sines Or the sine rule:

14. the law of cosines or the cosine rule

a² = b² + c² – 2bc cosA

b² = a² + c² – 2ac cosB

c² = b² + a² – 2abcosC

15. the projection formula

a = bcosC + ccosB

b = acosC + ccosA

c = bcosA + acosB

Algebraic identities.

Trig formulas.

Trig functions.

Trig equations.