解決(sinθ+cosθ)^2+(sinθ-cosθ)^2 |Microsoft數學求解器

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

因式分解

$$2$$

解題步驟

使用二項式定理 \left(a+b\right)^{2}=a^{2}+2ab+b^{2} 展開 \left(\sin(\theta )+\cos(\theta )\right)^{2}。

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

使用二項式定理 \left(a-b\right)^{2}=a^{2}-2ab+b^{2} 展開 \left(\sin(\theta )-\cos(\theta )\right)^{2}。

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

合併 \left(\sin(\theta )\right)^{2} 和 \left(\sin(\theta )\right)^{2} 以取得 2\left(\sin(\theta )\right)^{2}。

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

合併 2\sin(\theta )\cos(\theta ) 和 -2\sin(\theta )\cos(\theta ) 以取得 0。

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

合併 \left(\cos(\theta )\right)^{2} 和 \left(\cos(\theta )\right)^{2} 以取得 2\left(\cos(\theta )\right)^{2}。

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

因式分解 2。

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

評估

$$2$$