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Simplify the trigonometric expression $\frac{1-\cos\left(4x\right)}{1+\cos\left(2x\right)}$

Step-by-step Solution

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Final Answer

$4\sin\left(x\right)^2$
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Step-by-step Solution

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Applying an identity of double-angle cosine: $\cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2$

$\frac{1-\cos\left(4x\right)}{2-2\sin\left(x\right)^2}$

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

$\frac{1-\cos\left(4x\right)}{2-2\sin\left(x\right)^2}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (1-cos(4x))/(1+cos(2x)). Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. Factor the polynomial 2-2\sin\left(x\right)^2 by it's greatest common factor (GCF): 2. Applying the trigonometric identity: 1-\sin\left(\theta \right)^2 = \cos\left(\theta \right)^2. Use the trigonometric identity: 1-\cos\left(2x\right)=2\sin\left(x\right)^2.

Final Answer

$4\sin\left(x\right)^2$

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Plotting: $4\sin\left(x\right)^2$

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7
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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

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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.

Used Formulas

1. See formulas

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