Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Prove that, for any real
x
x
x
such that
x
≠
(
2
n
+
1
)
π
2
,
n
∈
Z
x\neq \dfrac{(2n+1)\pi}{2},\;n\in\mathbb Z
x
=
2
(
2
n
+
1
)
π
,
n
∈
Z
, the following identity holds:
sin
x
+
sin
3
x
cos
x
+
cos
3
x
=
tan
2
x
.
\frac{\sin x+\sin 3x}{\cos x+\cos 3x}=\tan 2x.
cos
x
+
cos
3
x
sin
x
+
sin
3
x
=
tan
2
x
.
Browse the problem library