ແກ້ (sinθ+cosθ)^2+(sinθ-cosθ)^2

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

ຕົວປະກອບ

$$2$$

ຂັ້ນຕອນການແກ້

ໃຊ້ທິດສະດີທະວິນາມ \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ເພື່ອຂະຫຍາຍ \left(\sin(\theta )+\cos(\theta )\right)^{2}.

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

ໃຊ້ທິດສະດີທະວິນາມ \left(a-b\right)^{2}=a^{2}-2ab+b^{2} ເພື່ອຂະຫຍາຍ \left(\sin(\theta )-\cos(\theta )\right)^{2}.

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

ຮວມ \left(\sin(\theta )\right)^{2} ແລະ \left(\sin(\theta )\right)^{2} ເພື່ອຮັບ 2\left(\sin(\theta )\right)^{2}.

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

ຮວມ 2\sin(\theta )\cos(\theta ) ແລະ -2\sin(\theta )\cos(\theta ) ເພື່ອຮັບ 0.

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

ຮວມ \left(\cos(\theta )\right)^{2} ແລະ \left(\cos(\theta )\right)^{2} ເພື່ອຮັບ 2\left(\cos(\theta )\right)^{2}.

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

ຕົວປະກອບຈາກ 2.

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

ປະເມີນ

$$2$$