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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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Solution

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Final Answer

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

Problem to solve:

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

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1

Multiply both sides of the equation by $\sin$

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

Learn how to solve definite integrals problems step by step online.

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

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Learn how to solve definite integrals 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

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

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0
a
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n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main topic:

Definite Integrals

Used formulas:

2. See formulas

Related topics:

Definite IntegralsIntegral CalculusCalculus

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