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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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  • Express in terms of sine and cosine
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  • Simplify into a single function
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  • Express in terms of Cotangent
  • Express in terms of Secant
  • Express in terms of Cosecant
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Multiply both sides of the equation by $\sin$

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

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

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Learn how to solve problems step by step online. Solve the trigonometric equation csc(x)+sin(x)=cot(x)cos(x). Multiply both sides of the equation by \sin. Simplify \sin\left(x\right)\cot\left(x\right)\cos\left(x\right) into \cos(x) by applying trigonometric identities. When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents. Multiplying polynomials \sin\left(x\right) and \csc\left(x\right)+\sin\left(x\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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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

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