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

Step-by-step Solution

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Final Answer

$\frac{\left(\cos\left(x\right)+1\right)\left(1-\cos\left(x\right)\right)}{\sin\left(x\right)}$
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Step-by-step Solution

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

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression ((1-cos(x))(1+1/cos(x)))/(sin(x)/cos(x)). Divide fractions \frac{\left(1-\cos\left(x\right)\right)\left(1+\frac{1}{\cos\left(x\right)}\right)}{\frac{\sin\left(x\right)}{\cos\left(x\right)}} 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}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Multiplying the fraction by \left(1-\cos\left(x\right)\right)\cos\left(x\right). Simplify the fraction \frac{\left(\cos\left(x\right)+1\right)\left(1-\cos\left(x\right)\right)\cos\left(x\right)}{\cos\left(x\right)} by \cos\left(x\right).

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifySimplify into a single functionExpress in terms of SineExpress in terms of CosineExpress in terms of TangentExpress in terms of CotangentExpress in terms of SecantExpress in terms of CosecantFactorFind the derivativeSolve (1+-1cosx)(1+1/cosx)/(sinx/cosx) using basic integrals

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Plotting: $\frac{\left(\cos\left(x\right)+1\right)\left(1-\cos\left(x\right)\right)}{\sin\left(x\right)}$

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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

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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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