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

Step-by-step Solution

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Final Answer

$\sin\left(x\right)^2$
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Step-by-step Solution

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

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

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

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

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sin(x)^2-cos(x)^2)/(1-cot(x)^2). Applying the trigonometric identity: \sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right). Apply the trigonometric identity: \cot(x)=\frac{\cos(x)}{\sin(x)}. Combine 1+\frac{-\cos\left(x\right)^2}{\sin\left(x\right)^2} in a single fraction. Divide fractions \frac{-\cos\left(2x\right)}{\frac{-\cos\left(x\right)^2+\sin\left(x\right)^2}{\sin\left(x\right)^2}} 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}.

Final Answer

$\sin\left(x\right)^2$

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Plotting: $\sin\left(x\right)^2$

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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

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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