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trigonometric
和差角公式
cos
(
a
+
b
)
=
cos
a
cos
b
−
sin
a
sin
b
cos
(
a
−
b
)
=
cos
a
cos
b
+
sin
a
sin
b
sin
(
a
+
b
)
=
sin
a
cos
b
+
cos
a
sin
b
sin
(
a
−
b
)
=
sin
a
cos
b
−
cos
a
sin
b
tan
(
a
+
b
)
=
tan
a
+
tan
b
1
−
tan
a
tan
b
tan
(
a
−
b
)
=
tan
a
−
tan
b
1
+
tan
a
tan
b
\begin{aligned} \cos(a+b) = \cos a\cos b - \sin a\sin b \\ \cos(a-b) = \cos a\cos b + \sin a\sin b \\ \sin(a+b) = \sin a\cos b + \cos a\sin b \\ \sin(a-b) = \sin a\cos b - \cos a\sin b \\ \tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} \\ \tan(a-b) = \frac{\tan a - \tan b}{1 + \tan a \tan b} \end{aligned}
cos
(
a
+
b
)
=
cos
a
cos
b
−
sin
a
sin
b
cos
(
a
−
b
)
=
cos
a
cos
b
+
sin
a
sin
b
sin
(
a
+
b
)
=
sin
a
cos
b
+
cos
a
sin
b
sin
(
a
−
b
)
=
sin
a
cos
b
−
cos
a
sin
b
tan
(
a
+
b
)
=
1
−
tan
a
tan
b
tan
a
+
tan
b
tan
(
a
−
b
)
=
1
+
tan
a
tan
b
tan
a
−
tan
b
积分公式
∫
−
T
2
T
2
cos
(
n
ω
t
)
sin
(
m
ω
t
)
d
t
=
0
∫
−
T
2
T
2
cos
(
n
ω
t
)
cos
(
m
ω
t
)
d
t
=
{
T
2
,
n
=
m
0
,
n
≠
m
∫
−
T
2
T
2
sin
(
n
ω
t
)
sin
(
m
ω
t
)
d
t
=
{
0
,
n
=
m
T
2
,
n
≠
m
\begin{aligned} \int_{-\frac{T}{2}}^{\frac{T}{2}} \cos(n\omega t)\sin(m\omega t)dt &=& 0 \\ \int_{-\frac{T}{2}}^{\frac{T}{2}} \cos(n\omega t)\cos(m\omega t)dt &=& \begin{cases} \frac{T}{2}, && n = m \\ 0, && n \neq m \end{cases} \\ \int_{-\frac{T}{2}}^{\frac{T}{2}} \sin(n\omega t)\sin(m\omega t)dt &=& \begin{cases} 0, && n = m \\ \frac{T}{2}, && n \neq m \end{cases} \end{aligned}
∫
−
2
T
2
T
cos
(
nω
t
)
sin
(
mω
t
)
d
t
∫
−
2
T
2
T
cos
(
nω
t
)
cos
(
mω
t
)
d
t
∫
−
2
T
2
T
sin
(
nω
t
)
sin
(
mω
t
)
d
t
=
=
=
0
{
2
T
,
0
,
n
=
m
n
=
m
{
0
,
2
T
,
n
=
m
n
=
m
Previous
Formula
Last updated
2 years ago