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

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Final answer to the problem

$-\csc\left(x\right)$
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Combine $\sin\left(-x\right)+\frac{\sin\left(-x\right)}{\cos\left(-x\right)}$ in a single fraction

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (1+1/cos(-x))/(sin(-x)+sin(-x)/cos(-x)). Combine \sin\left(-x\right)+\frac{\sin\left(-x\right)}{\cos\left(-x\right)} in a single fraction. Divide fractions \frac{1+\frac{1}{\cos\left(-x\right)}}{\frac{-\sin\left(x\right)-\sin\left(x\right)\cos\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}. Factor the polynomial -\sin\left(x\right)-\sin\left(x\right)\cos\left(x\right) by it's greatest common factor (GCF): -\sin\left(x\right). Combine all terms into a single fraction with \cos\left(x\right) as common denominator.

Final answer to the problem

$-\csc\left(x\right)$

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Function Plot

Plotting: $-\csc\left(x\right)$

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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.

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