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Simplify the trigonometric expression $\frac{\frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)}}{1-\cos\left(a\right)}$

Step-by-step Solution

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Final Answer

$\csc\left(a\right)^2$
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Step-by-step Solution

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Divide fractions $\frac{\frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)}}{1-\cos\left(a\right)}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$

$\frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)\left(1-\cos\left(a\right)\right)}$

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$\frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)\left(1-\cos\left(a\right)\right)}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (((1-cos(a))/sin(a))/sin(a))/(1-cos(a)). Divide fractions \frac{\frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)}}{1-\cos\left(a\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}. Divide fractions \frac{\frac{1-\cos\left(a\right)}{\sin\left(a\right)}}{\sin\left(a\right)\left(1-\cos\left(a\right)\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}. Simplify the fraction \frac{1-\cos\left(a\right)}{\sin\left(a\right)^2\left(1-\cos\left(a\right)\right)} by 1-\cos\left(a\right). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

Final Answer

$\csc\left(a\right)^2$

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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.

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