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Expand and simplify the trigonometric expression $\left(-\sin\left(x\right)+\cos\left(x\right)+2\right)\left(-\cos\left(x\right)-\sin\left(x\right)\right)$

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Solution

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Final Answer

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

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Multiply the single term $-\cos\left(x\right)-\sin\left(x\right)$ by each term of the polynomial $\left(-\sin\left(x\right)+\cos\left(x\right)+2\right)$

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

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

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Learn how to solve integral calculus problems step by step online. Expand and simplify the trigonometric expression (-sin(x)+cos(x)+2)(-cos(x)-sin(x)). Multiply the single term -\cos\left(x\right)-\sin\left(x\right) by each term of the polynomial \left(-\sin\left(x\right)+\cos\left(x\right)+2\right). Multiply the single term -\sin\left(x\right) by each term of the polynomial \left(-\cos\left(x\right)-\sin\left(x\right)\right). Multiply the single term \cos\left(x\right) by each term of the polynomial \left(-\cos\left(x\right)-\sin\left(x\right)\right). Multiply the single term 2 by each term of the polynomial \left(-\cos\left(x\right)-\sin\left(x\right)\right).

Final Answer

$-\cos\left(2x\right)-2\cos\left(x\right)-2\sin\left(x\right)$

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Product of Binomials with Common TermFOIL MethodFactorFind the derivativeFind the integral

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

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a
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f
g
m
n
u
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x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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