Mathematical Formulas

1. TRIGONOMETRIC IDENTITIES HAZBER SAMSON
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