Statement-1: If $\vec a$ and $\vec b$ are two unit vectors, then $|\vec a+\vec b|^2+|\vec a-\vec b|^2=4$

Statement-2: If a and b are two unit vectors inclined at an angle θ, then the unit vectors along their sum and difference are $\frac{\vec a+\vec b}{2 \cos θ/2}$ and $\frac{\vec a-\vec b}{2 \sin θ/2}$ respectively.

Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1.

We have,

$|\vec a+\vec b|^2+|\vec a-\vec b|^2=2(|\vec a|^2+|\vec b|^2)$

$⇒|\vec a+\vec b|^2+|\vec a-\vec b|^2=2(1+1)=4$

So, statement-1 is true.

Since, $\vec a$ and $\vec b$ are unit vectors inclined at an angle θ.

$∴|\vec a+\vec b|^2+|\vec a|^2+|\vec b|^2+2(\vec a.\vec b)$

$=|\vec b|^2+|\vec b|^2+|\vec a||\vec b|\cos θ$

$⇒|\vec a+\vec b|^2=2+2\cos θ=2(1+\cos θ)=4\cos^2 θ/2$ and, $|\vec a-\vec b|^2=4\sin^2 θ/2$

Therefore, unit vectors along $\vec a+\vec b$ and $\vec a-\vec b$ are $\frac{\vec a+\vec b}{2 \cos θ/2}$ and $\frac{\vec a-\vec b}{2 \sin θ/2}$ respectively.

So, statement-2 is true.