Riješi (sinθ+cosθ)^2+(sinθ-cosθ)^2

$$( \sin \theta + \cos \theta ) ^ { 2 } + ( \sin \theta - \cos \theta ) ^ { 2 }$$

Faktor

$$2$$

Koraci rješenja

Upotrijebite binomni teorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} da biste proširili \left(\sin(\theta )+\cos(\theta )\right)^{2}.

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

Upotrijebite binomni teorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} da biste proširili \left(\sin(\theta )-\cos(\theta )\right)^{2}.

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

Kombinirajte \left(\sin(\theta )\right)^{2} i \left(\sin(\theta )\right)^{2} da biste dobili 2\left(\sin(\theta )\right)^{2}.

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

Kombinirajte 2\sin(\theta )\cos(\theta ) i -2\sin(\theta )\cos(\theta ) da biste dobili 0.

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

Kombinirajte \left(\cos(\theta )\right)^{2} i \left(\cos(\theta )\right)^{2} da biste dobili 2\left(\cos(\theta )\right)^{2}.

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

Izlučite 2.

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

Izračunaj

$$2$$