Trigonometric Identities With Fundamental Identities
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1Trigonometric Identities
FUNDAMENTAL IDENTITIES
SUM AND DIFFERENCE IDENTITIES
sin(
A
B
)
sin
A
cos
B
cos
A
sin
B
sin
A
1
cos
A
tan
A
cot
A
sin(
A
B
)
sin
A
cos
B
cos
A
sin
B
cos
A
tan
A
sin
A
1
1
cos(
A
B
)
cos
A
cos
B
sin
A
sin
B
sec
A
csc
A
cos
A
sin
A
cos(
A
B
)
cos
A
cos
B
sin
A
sin
B
sin(
A
)
sin
A
cos(
A
)
cos
A
tan
A
tan
B
tan(
A
)
tan
A
cot(
A
)
cot
A
tan(
A
B
)
1
tan
A
tan
B
sec(
A
)
sec
A
csc(
A
)
csc
A
tan
A
tan
B
2
2
tan(
A
B
)
sin
A
cos
A
1
1
tan
A
tan
B
2
2
tan
A
1
sec
A
2
2
1
cot
A
csc
A
DOUBLE-ANGLE IDENTITIES
HALF-ANGLE IDENTITIES
sin
2
A
2
sin
A
cos
A
A
1
cos
A
A
1
cos
A
sin
tan
2
2
cos
2
A
cos
A
sin
A
2
2
2
1
cos
A
A
1
cos
A
A
sin
A
2
cos
2
A
1
2
sin
A
cos
tan
2
2
2
1
cos
A
2
cos
2
A
2
cos
1
A
1
cos
A
2
tan
A
tan
tan
2
A
2
sin
A
2
1
tan
A
COFUNCTION IDENTITIES
SUM-TO-PRODUCT AND PRODUCT-TO-SUM
1
sin(
90
A
)
cos
A
sin(
A
)
cos
A
sin
A
sin
B
[cos(
A
B
)
cos(
A
B
)]
2
2
cos(
90
A
)
sin
A
cos(
A
)
sin
A
1
sin
A
cos
B
[sin(
A
B
)
sin(
A
B
)]
2
2
tan(
90
A
)
cot
A
tan(
A
)
cot
A
1
cos
A
cos
B
[cos(
A
B
)
cos(
A
B
)]
2
2
cot(
90
A
)
tan
A
cot(
A
)
tan
A
A
B
A
B
2
sin
A
sin
B
2
sin
cos
sec(
90
A
)
csc
A
sec(
A
)
csc
A
2
2
2
csc(
90
A
)
sec
A
csc(
A
)
sec
A
A
B
A
B
2
sin
A
sin
B
2
cos
sin
SOLVING TRIANGLES
2
2
Law of Sines:
A
B
A
B
cos
A
cos
B
2
cos
cos
sin
A
sin
B
sin
C
2
2
a
b
c
A
B
A
B
Law of Cosines:
cos
A
cos
B
2
sin
sin
2
2
2
2
2
a
b
c
2
bc
cos
A
1
cos
2
A
2
2
2
b
a
c
2
ac
cos
B
2
sin
A
2
2
2
2
c
a
b
2
ab
cos
C
1
cos
2
A
2
cos
A
2
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