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Solve the trigonometric equation $\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cos\left(x\right)$

Step-by-step Solution

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Final answer to the problem

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution

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Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$\csc\left(x\right)+\sin\left(x\right)-\cot\left(x\right)\cos\left(x\right)=0$

Learn how to solve integrals of rational functions problems step by step online.

$\csc\left(x\right)+\sin\left(x\right)-\cot\left(x\right)\cos\left(x\right)=0$

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Learn how to solve integrals of rational functions problems step by step online. Solve the trigonometric equation csc(x)+sin(x)=cot(x)cos(x). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \cos\left(x\right). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

Final answer to the problem

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$

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Function Plot

Plotting: $\csc\left(x\right)+\sin\left(x\right)-\cot\left(x\right)\cos\left(x\right)$

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7
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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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

Used Formulas

See formulas (1)

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