TRIGONOMETRIC IDENTITIES

TRIGONOMETRIC IDENTITIES

1. RECIPRIOCAL: csc0=1/sin0 sec0=1/cos0 cot0=1/tan0

2. QUOTIENT: tan0=sin0/cos0 cot0=cos0/sin0

3. PYTHAGOREAN: cos^20+sin^20=1 1+tan^20=sec^20 cot^20+1=csc^20

4. EVEN ODDS: sin(-0)=-sin0 csc(-0)=-csc0 cos(-0)=cos0 sec(-0)=sec0 tan(-0)=-tan0 cot(-0)=-cot(0)

5. Sum and difference

   • Sin( a+b)= sinacosb+sinacosb Sin(a-b)=sinacosb-sinacosb
   • Cos(a+b)= cosacosb-sinasinb Cos(a-b)= cosacosb+sinasinb
   • tan(a+b)= (tana+tanb)/(1-(tanatanb)) tan(a-b)= (tana-tanb)/(1+(tanatanb))

6. Double-angle formula: sin(20)=2sin0cos0 cos(20)=cos^20-sin^20 tan(20)=2tan0/1-tan^20

7. Half-angle Formula: sin 0/2= (1-cos0)/2 cos 0/2= (1+cos0)/2 tan 0/2= (1-cos0)/sin0