Let →a and →b be two unit vectors such that →a⋅→b=0. For some x,y∈R, let →c=x→a+y→b+(→a×→b). If |→c|=2 and the vector →c is inclined at the same angle α to both →a and →b, then the value of 8cos2α is .

Let →a and →b be two unit vectors such that →a⋅→b=0. For som

1.	Let →a and →b be two unit vectors such that →a⋅→b=0. For some x,y∈R, let →c=x→a+y→b+(→a×→b). If \|→c\|=2 and the vector →c is inclined at the same angle α to both →a and →b, then the value of 8cos2α is .
Answer» Let $\to a$ and $\to b$ be two unit vectors such that $\to a \cdot \to b = 0$ . For some $x, y \in R$ , let $\to c = x \to a + y \to b + (\to a \times \to b)$ . If $\| \to c \| = 2$ and the vector $\to c$ is inclined at the same angle $α$ to both $\to a$ and $\to b$ , then the value of $8 {cos}^{2} α$ is .