Expand and simplify the trigonometric expression $\cos\left(x\right)^4\left(-2\cot\left(2x\right)^2\csc\left(2x\right)-2\csc\left(2x\right)^3\right)$

Step-by-step Solution

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Final answer to the problem

$-2\cot\left(2x\right)^2\csc\left(2x\right)\cos\left(x\right)^4-2\csc\left(2x\right)^3\cos\left(x\right)^4$
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Step-by-step Solution

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  • Product of Binomials with Common Term
  • FOIL Method
  • Find the integral
  • Find the derivative
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  • Integrate by partial fractions
  • Integrate by substitution
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  • Integrate using tabular integration
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Multiply the single term $\cos\left(x\right)^4$ by each term of the polynomial $\left(-2\cot\left(2x\right)^2\csc\left(2x\right)-2\csc\left(2x\right)^3\right)$

$-2\cot\left(2x\right)^2\csc\left(2x\right)\cos\left(x\right)^4-2\csc\left(2x\right)^3\cos\left(x\right)^4$

Final answer to the problem

$-2\cot\left(2x\right)^2\csc\left(2x\right)\cos\left(x\right)^4-2\csc\left(2x\right)^3\cos\left(x\right)^4$

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Function Plot

Plotting: $-2\cot\left(2x\right)^2\csc\left(2x\right)\cos\left(x\right)^4-2\csc\left(2x\right)^3\cos\left(x\right)^4$

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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: 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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