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Simplify the trigonometric expression $\cos\left(2x\right)^2\cos\left(2x\right)$

Step-by-step Solution

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Final answer to the problem

$\frac{8\tan\left(x\right)^{3}}{\left(1+\tan\left(x\right)^2\right)^{3}}$
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Step-by-step Solution

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When multiplying exponents with same base you can add the exponents: $\cos\left(2x\right)^2\cos\left(2x\right)$

$\cos\left(2x\right)^{3}$

Learn how to solve simplify trigonometric expressions problems step by step online.

$\cos\left(2x\right)^{3}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression cos(2x)^2cos(2x). When multiplying exponents with same base you can add the exponents: \cos\left(2x\right)^2\cos\left(2x\right). Apply the trigonometric identity: \cos\left(2\theta \right)=\frac{2\tan\left(\theta \right)}{1+\tan\left(\theta \right)^2}. 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}. The power of a product is equal to the product of it's factors raised to the same power.

Final answer to the problem

$\frac{8\tan\left(x\right)^{3}}{\left(1+\tan\left(x\right)^2\right)^{3}}$

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

Express in terms of sine and cosineSimplifySimplify into a single functionExpress in terms of SineExpress in terms of CosineExpress in terms of CotangentExpress in terms of SecantExpress in terms of CosecantFactorFind the derivativeSolve cos2x^2cos2x using basic integrals

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Function Plot

Plotting: $\frac{8\tan\left(x\right)^{3}}{\left(1+\tan\left(x\right)^2\right)^{3}}$

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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: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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