👉 Try now NerdPal! Our new math app on iOS and Android

# Solve the trigonometric equation $\tan\left(2x\right)=1$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Videos

$x=\frac{1}{8}\pi+\frac{1}{2}\pi n,\:x=\frac{5}{8}\pi+\frac{1}{2}\pi n\:,\:\:n\in\Z$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\tan\left(2x\right)=1$

Specify the solving method

1

The angles where the function $\tan\left(2x\right)$ is $1$ are

$2x=45^{\circ}+360^{\circ}n,\:2x=225^{\circ}+360^{\circ}n$

Learn how to solve trigonometric equations problems step by step online.

$2x=45^{\circ}+360^{\circ}n,\:2x=225^{\circ}+360^{\circ}n$

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation tan(2x)=1. The angles where the function \tan\left(2x\right) is 1 are. Solve the equation (1). Divide both sides of the equation by 2. Simplifying the quotients.

$x=\frac{1}{8}\pi+\frac{1}{2}\pi n,\:x=\frac{5}{8}\pi+\frac{1}{2}\pi n\:,\:\:n\in\Z$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Verify if true (using algebra)Verify if true (using arithmetic)

SnapXam A2

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Trigonometric Equations

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account