Trigonometric Identities
1) Reciprocal Identities
a.
csc u=1
sin u∨sin u ∙ csc u=1
b.
secu=1
cos u∨cos u ∙ sec u=1
c.
cot u=1
tan u∨tan u ∙ cot u=1
2) Quotient Identities
a.
tan u=sin u
cos u
b.
tan u=sec u
csc u
c.
cot u=cos u
sin u
d.
cot u=cscu
secu
3) Pythagorean Identities
a.
sin2u+cos2u=1
b.
1+tan
2
u=sec
2
u
c.
1+cot2u=csc2u
4) Odd and Even Function Identities
a.
sin
(
−u
)
=−sin u
(
ODD
)
b.
cos
(
−u
)
=cos u(EVEN )
c.
tan
(
−u
)
=−tan u(ODD )
d.
csc
(
−u
)
=−csc u(ODD )
e.
sec
(
−u
)
=secu
(
EVEN
)
f.
cot
(
−u
)
=−cot u(ODD)
5) Co- Function Identities
a.
sin
(
π
2−u
)
=cos u
b.
cos
(
π
2−u
)
=sin u
c.
tan
(
π
2−u
)
=cot u
d.
cot
(
π
2−u
)
=tan u
e.
sec
(
π
2−u
)
=c s c u
f.
csc
(
π
2−u
)
=secu
6) Composite Argument Identities
a.
sin
(
α+β
)
=sin α ∙ cos β+cos α ∙ sin β
b.
sin
(
α−β
)
=sin α ∙cos β−cos α ∙ sin β
c.
cos
(
α+β
)
=cos α ∙ cos β−sin α ∙ sin β
d.
cos
(
α−β
)
=cos α ∙ cos β+sin α ∙ sin β
e.
tan
(
α+β
)
=tan α+tan β
1−tan α ∙ tan β
f.
tan
(
α−β
)
=tan α−tan β
1+tan α ∙ tan β
7) Double- Angle Argument identities
a.
sin
(
2u
)
=2 sin u ∙ cos u
b.
cos
(
2u
)
=cos
2
u−sin
2
u
c.
cos
(
2u
)
=1−2 sin
2
u
d.
cos
(
2u
)
=2cos
2
u−1
e.
tan
(
2u
)
=2 tan u
1−tan
2
u
8) Power Reducing Identities
