求解 (sinθ+cosθ)^2+(sinθ-cosθ)^2

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

因式分解

$$2$$

求解步骤

使用二项式定理 \left(a+b\right)^{2}=a^{2}+2ab+b^{2} 展开 \left(\sin(\theta )+\cos(\theta )\right)^{2}。

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

使用二项式定理 \left(a-b\right)^{2}=a^{2}-2ab+b^{2} 展开 \left(\sin(\theta )-\cos(\theta )\right)^{2}。

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

合并 \left(\sin(\theta )\right)^{2} 和 \left(\sin(\theta )\right)^{2}，得到 2\left(\sin(\theta )\right)^{2}。

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

合并 2\sin(\theta )\cos(\theta ) 和 -2\sin(\theta )\cos(\theta )，得到 0。

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

合并 \left(\cos(\theta )\right)^{2} 和 \left(\cos(\theta )\right)^{2}，得到 2\left(\cos(\theta )\right)^{2}。

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

因式分解出 2。

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

求值

$$2$$