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Simplify the trigonometric expression $\frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)}$

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Solution

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Final Answer

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

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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$

$\frac{\left(\left(\cos\left(x\right)^3\right)^{\frac{1}{3}}+\left(-\sin\left(x\right)^3\right)^{\frac{1}{3}}\right)\left(\left(\cos\left(x\right)^3\right)^{\frac{2}{3}}-\left(\cos\left(x\right)^3\right)^{\frac{1}{3}}\left(-\sin\left(x\right)^3\right)^{\frac{1}{3}}+\left(\sin\left(x\right)^3\right)^{\frac{2}{3}}\right)}{\cos\left(x\right)-\sin\left(x\right)}$

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$\frac{\left(\left(\cos\left(x\right)^3\right)^{\frac{1}{3}}+\left(-\sin\left(x\right)^3\right)^{\frac{1}{3}}\right)\left(\left(\cos\left(x\right)^3\right)^{\frac{2}{3}}-\left(\cos\left(x\right)^3\right)^{\frac{1}{3}}\left(-\sin\left(x\right)^3\right)^{\frac{1}{3}}+\left(\sin\left(x\right)^3\right)^{\frac{2}{3}}\right)}{\cos\left(x\right)-\sin\left(x\right)}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (cos(x)^3-sin(x)^3)/(cos(x)-sin(x)). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Divide 1 by 3. Divide 1 by 3. Divide 2 by 3.

Final Answer

$1+\cos\left(x\right)\sin\left(x\right)$

Explore different ways to solve this problem

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

Express in terms of sine and cosineSimplifySimplify 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 (cosx^3+-1sinx^3)/(cosx+-1sinx) using basic integrals

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Plotting: $1+\cos\left(x\right)\sin\left(x\right)$

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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
D□x
∫
∫◻
|◻|
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

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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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