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

Step-by-step Solution

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Final Answer

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

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1

Apply the property of the quotient of two powers with the same exponent, inversely: $\frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m$, where $m$ equals $2$

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

Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$

$\tan\left(x\right)^2$
Why is sin(x)/cos(x) = tan(x) ?

Final Answer

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

Explore different ways to solve this problem

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Express in terms of sine and cosineSimplifyExpress 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 (sinx^2)/(cosx^2) using basic integrals

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

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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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