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

Step-by-step Solution

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Final answer to the problem

$x=\frac{1}{8}\pi+\frac{1}{2}\pi n,\:x=\frac{5}{8}\pi+\frac{1}{2}\pi n\:,\:\:n\in\Z$
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Step-by-step Solution

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1

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

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

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

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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. Expand the fraction \frac{45+180n}{2} into 2 simpler fractions with common denominator 2.

Final answer to the problem

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

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Function Plot

Plotting: $\tan\left(2x\right)-1$

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1
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5
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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

How to improve your answer:

Main Topic: Trigonometric Equations

A trigonometric equation is an equation in which one or more trigonometric ratios appear.

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