Simplify the trigonometric expression $\frac{\tan\left(x\right)^2-\sin\left(x\right)^2}{\cot\left(x\right)^2-\cos\left(x\right)^2}$

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Final answer to the problem

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

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  • Find the derivative
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Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

$\frac{\tan\left(x\right)^2-\sin\left(x\right)^2}{\frac{\cos\left(x\right)^2}{\sin\left(x\right)^2}-\cos\left(x\right)^2}$
Why is cot(x) = cos(x)/sin(x) ?

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (tan(x)^2-sin(x)^2)/(cot(x)^2-cos(x)^2). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Combine \frac{\cos\left(x\right)^2}{\sin\left(x\right)^2}-\cos\left(x\right)^2 in a single fraction. Divide fractions \frac{\tan\left(x\right)^2-\sin\left(x\right)^2}{\frac{\cos\left(x\right)^2-\cos\left(x\right)^2\sin\left(x\right)^2}{\sin\left(x\right)^2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Factor the polynomial \cos\left(x\right)^2-\cos\left(x\right)^2\sin\left(x\right)^2 by it's greatest common factor (GCF): \cos\left(x\right)^2.

Final answer to the problem

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

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Function Plot

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

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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.

Used Formulas

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