Simplify the expression $f\left(x\right)=\left(\sin\left(x\right)-\cos\left(x\right)\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)+2\cos\left(x\right)^2$

Step-by-step Solution

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Final answer to the problem

$f\left(x\right)=1$
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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: $(a+b)(a-b)=a^2-b^2$.

Learn how to solve factor by difference of squares problems step by step online.

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

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Learn how to solve factor by difference of squares problems step by step online. Simplify the expression f(x)=(sin(x)-cos(x))(sin(x)+cos(x))+2cos(x)^2. 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.. Combining like terms -\cos\left(x\right)^2 and 2\cos\left(x\right)^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1.

Final answer to the problem

$f\left(x\right)=1$

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Function Plot

Plotting: $f\left(x\right)-\left(\sin\left(x\right)-\cos\left(x\right)\right)\left(\sin\left(x\right)+\cos\left(x\right)\right)-2\cos\left(x\right)^2$

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a
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(◻)
+
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×
◻/◻
/
÷
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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.

Used Formulas

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