Solve the equation $y=\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(\cos\left(x\right)-\sin\left(x\right)\right)$

Step-by-step Solution

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Final answer to the problem

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

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  • Differential
  • Find the derivative
  • Find the integral
  • Find the derivative using the definition
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The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.

$y=\cos\left(x\right)^2-\sin\left(x\right)^2$

Final answer to the problem

$y=\cos\left(x\right)^2-\sin\left(x\right)^2$

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Function Plot

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

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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: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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