👉 Try now NerdPal! Our new math app on iOS and Android

Simplify the expression $\frac{\sin\left(x\right)\cos\left(x\right)^4\tan\left(x\right)^4}{\sqrt[3]{x}}$

Step-by-step Solution

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

$\frac{\sin\left(x\right)^{5}}{\sqrt[3]{x}}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\sin\left(x\right)\cos\left(x\right)^4\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)^4}{\sqrt[3]{x}}$
Why is tan(x) = sin(x)/cos(x) ?

Learn how to solve simplification of algebraic fractions problems step by step online.

$\frac{\sin\left(x\right)\cos\left(x\right)^4\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)^4}{\sqrt[3]{x}}$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression (sin(x)cos(x)^4tan(x)^4)/(x^1/3). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Multiplying the fraction by \sin\left(x\right)\cos\left(x\right)^4. When multiplying exponents with same base you can add the exponents: \sin\left(x\right)^4\sin\left(x\right).

Final Answer

$\frac{\sin\left(x\right)^{5}}{\sqrt[3]{x}}$

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

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind sinxcosx^4/(x^0.3333) using the definitionSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

Give us your feedback!

Function Plot

Plotting: $\frac{\sin\left(x\right)^{5}}{\sqrt[3]{x}}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

Used Formulas

1. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account