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Simplify the trigonometric expression $\frac{\cot\left(x\right)}{\csc\left(x\right)-\sin\left(x\right)}$

Step-by-step Solution

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Final Answer

$\sec\left(x\right)$
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Step-by-step Solution

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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$

$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\csc\left(x\right)-\sin\left(x\right)}$
Why does cot(x) = cos(x)/sin(x) ?

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$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\csc\left(x\right)-\sin\left(x\right)}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression cot(x)/(csc(x)-sin(x)). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Divide fractions \frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\csc\left(x\right)-\sin\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(\csc\left(x\right)-\sin\left(x\right)\right). Applying the trigonometric identity: \sin\left(\theta \right)\csc\left(\theta \right) = 1.

Final Answer

$\sec\left(x\right)$

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1
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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: 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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