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

Step-by-step Solution

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Final Answer

$\frac{1-2\cos\left(x\right)\sin\left(x\right)}{\left(\cos\left(x\right)-\sin\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)}$
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Step-by-step Solution

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Rewrite $1-\tan\left(x\right)$ in terms of sine and cosine functions

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

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression tan(x)/(1-tan(x))+cot(x)/(1-cot(x)). Rewrite 1-\tan\left(x\right) in terms of sine and cosine functions. Divide fractions \frac{\tan\left(x\right)}{\frac{\cos\left(x\right)-\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}. Applying the trigonometric identity: \tan\left(\theta \right)\cos\left(\theta \right) = \sin\left(\theta \right). Rewrite 1-\cot\left(x\right) in terms of sine and cosine functions.

Final Answer

$\frac{1-2\cos\left(x\right)\sin\left(x\right)}{\left(\cos\left(x\right)-\sin\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)}$

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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 tanx/(1+-1tanx)+cotx/(1+-1cotx) using basic integrals

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Function Plot

Plotting: $\frac{1-2\cos\left(x\right)\sin\left(x\right)}{\left(\cos\left(x\right)-\sin\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)}$

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a
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m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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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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