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Trigonometric identities
- 1. TRIGONOMETRIC IDENTITIES HAZBERSAMSON TRIGONOMETRIC IDENTITIES Basic Formulas 1. θ θ sin 1 csc = , θ θ cos 1 sec = and θ θ tan 1 cot = 2. θ θ θ cos sin tan = and θ θ θ sin cos cot = 3. 122 =+ θθ CosSin 4. θθ 22 sectan1 =+ 5. θθ 22 csccot1 =+ Compound Angle Identities 6. ( ) βαβαβα sincoscossin +=+Sin 7. ( ) βαβαβα sincoscossin −=−Sin 8. ( ) βαβαβα sinsincoscos −=+Cos 9. ( ) βαβαβα sinsincoscos +=−Cos 10. ( ) βα βα βα tantan1 tantan − + =+Tan 11. ( ) βα βα βα tantan1 tantan + − =−Tan 12. ( ) θθ SinSin =− , ( ) θθ CosCos =− ( ) θθ TanTan −=− 13. ( ) ,2 θθπ SinSin =+ ( ) θθπ CosCos =+2 ( ) θθπ TanTan =+ Half-Angle Identities 14. 2 cos1 2 2 θθ − =Sin or 2 2cos12 θ θ − =Sin 15. 2 cos1 2 2 θθ + =Cos or 2 2cos12 θ θ + =Cos 16. θ θθ cos1 cos1 2 2 + − =Tan or θ θ θ 2cos1 2cos12 + − =Tan Double Angle Identities 17. θθθ cossin22 =Sin 2 cos 2 sin2 θθ θ =Sin 18. θθθ 22 sincos2 −=Cos 2 sin 2 cos 22 θθ θ −=Cos 19. θ θ θ 2 tan1 tan2 2 − =Tan 2 tan1 2 tan2 2 θ θ θ − =Tan Triple Angle Identities 20. θθθ 3 sin4sin33 −=Sin 21. θθθ cos3cos43 3 −=Cos 22. θ θθ θ 2 3 tan31 tantan3 3 − − =Tan Sums into Products 23. 22 2 BA Cos BA SinBSinASin −+ =+ 24. 22 2 BA Sin BA CosBSinASin −+ =− 25. 22 2 BA Cos BA CosBCosACos −+ =+ 26. 22 2 BA Sin BA SinBCosACos −+ −=− Product into Sums 27. ( ) ( )QPSinQPSinSinPCosQ −++=2 28. ( ) ( )QPSinQPSinCosPSinQ −−+=2 29. ( ) ( )QPCosQPCosCosPCosQ −++=2 30. ( ) ( )QPCosQPCosSinPSinQ −−+=− 2