Simplify the trigonometric expression $\frac{\sin\left(x\right)^2}{1+\cos\left(x\right)}$

Step-by-step Solution

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Final answer to the problem

$1-\cos\left(x\right)$
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Step-by-step Solution

How should I solve this problem?

  • Simplify into a single function
  • Find the derivative
  • Integrate using basic integrals
  • Verify if true (using algebra)
  • Verify if true (using arithmetic)
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Applying the trigonometric identity: $\sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2$

$\frac{1-\cos\left(x\right)^2}{1+\cos\left(x\right)}$
Why is 1 - cos(x)^2 = sin(x)^2 ?

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sin(x)^2)/(1+cos(x)). Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2. Factor the difference of squares 1-\cos\left(x\right)^2 as the product of two conjugated binomials. Simplify the fraction \frac{\left(1+\cos\left(x\right)\right)\left(1-\cos\left(x\right)\right)}{1+\cos\left(x\right)} by 1+\cos\left(x\right).

Final answer to the problem

$1-\cos\left(x\right)$

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Function Plot

Plotting: $1-\cos\left(x\right)$

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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

See formulas (2)

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