Solve (sinθ+cosθ)^2+(sinθ-cosθ)^2

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

Factor

$$2$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sin(\theta )+\cos(\theta )\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sin(\theta )-\cos(\theta )\right)^{2}.

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

Combine \left(\sin(\theta )\right)^{2} and \left(\sin(\theta )\right)^{2} to get 2\left(\sin(\theta )\right)^{2}.

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

Combine 2\sin(\theta )\cos(\theta ) and -2\sin(\theta )\cos(\theta ) to get 0.

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

Combine \left(\cos(\theta )\right)^{2} and \left(\cos(\theta )\right)^{2} to get 2\left(\cos(\theta )\right)^{2}.

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

Factor out 2.

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

Evaluate

$$2$$