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# Solve the trigonometric equation $8\sin\left(x\right)=2+\frac{4}{\csc\left(x\right)}$

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##  Final answer to the problem

$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Express in terms of sine and cosine
• Simplify
• Simplify into a single function
• Express in terms of Sine
• Express in terms of Cosine
• Express in terms of Tangent
• Express in terms of Cotangent
• Express in terms of Secant
• Express in terms of Cosecant
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The reciprocal sine function is cosecant: $\frac{1}{\csc(x)}=\sin(x)$

$8\sin\left(x\right)=2+4\sin\left(x\right)$

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$8\sin\left(x\right)=2+4\sin\left(x\right)$

Learn how to solve problems step by step online. Solve the trigonometric equation 8sin(x)=2+4/csc(x). The reciprocal sine function is cosecant: \frac{1}{\csc(x)}=\sin(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. Combining like terms 8\sin\left(x\right) and -4\sin\left(x\right). Divide both sides of the equation by 4.

##  Final answer to the problem

$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$

##  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

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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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