Question

Prove that : $(1+\sin \theta -\cos \theta {)}^2+(1-\sin \theta -\cos \theta {)}^2=4(1-\cos \theta )$

Answer 1

$\left[\right(1-\cos \theta )+\sin \theta {]}^2=[(1-\cos \theta )-\sin \theta {)}^2$

$(a+b{)}^2+(a-b{)}^2=2(a^2+b^2)=2(1+{\cos }^2\theta -2\cos \theta +{\sin }^2\theta )$

$=2(1+1-2\cos \theta )=4(1-\cos \theta )$.