ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

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

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
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

##  Final Answer

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

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.

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

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

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

##  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

Verify if true (using algebra)Verify if true (using arithmetic)

SnapXam A2

Go!
1
2
3
4
5
6
7
8
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

### Main topic:

Definite Integrals

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account