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

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Final answer to the problem

$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$
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Simplify $\cos\left(x\right)\csc\left(x\right)$ into $\cot(x)$ by applying trigonometric identities

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$\sec\left(x\right)\csc\left(x\right)+\cot\left(x\right)=\tan\left(x\right)+\cot\left(x\right)$

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Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation sec(x)csc(x)+cot(x)=tan(x)+cos(x)csc(x). Simplify \cos\left(x\right)\csc\left(x\right) into \cot(x) by applying trigonometric identities. 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. Cancel like terms \cot\left(x\right) and -\cot\left(x\right). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

Final answer to the problem

$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$

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Function Plot

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

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0
a
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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.

Used Formulas

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