Løs left(cos(x)+sin(x)right)^2+left(cos(x)-sin(x)right)^2

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

Faktoriser

$$2$$

Løsningsvejledning

Brug binomialsætningen \left(a+b\right)^{2}=a^{2}+2ab+b^{2} til at udvide \left(\cos(x)+\sin(x)\right)^{2}.

$$factor(\left(\cos(x)\right)^{2}+2\cos(x)\sin(x)+\left(\sin(x)\right)^{2}+\left(\cos(x)-\sin(x)\right)^{2})$$

Brug binomialsætningen \left(a-b\right)^{2}=a^{2}-2ab+b^{2} til at udvide \left(\cos(x)-\sin(x)\right)^{2}.

$$factor(\left(\cos(x)\right)^{2}+2\cos(x)\sin(x)+\left(\sin(x)\right)^{2}+\left(\cos(x)\right)^{2}-2\cos(x)\sin(x)+\left(\sin(x)\right)^{2})$$

Kombiner \left(\cos(x)\right)^{2} og \left(\cos(x)\right)^{2} for at få 2\left(\cos(x)\right)^{2}.

$$factor(2\left(\cos(x)\right)^{2}+2\cos(x)\sin(x)+\left(\sin(x)\right)^{2}-2\cos(x)\sin(x)+\left(\sin(x)\right)^{2})$$

Kombiner 2\cos(x)\sin(x) og -2\cos(x)\sin(x) for at få 0.

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

Kombiner \left(\sin(x)\right)^{2} og \left(\sin(x)\right)^{2} for at få 2\left(\sin(x)\right)^{2}.

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

Udfaktoriser 2.

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

Evaluer

$$2$$