Let unit vectors $\vec a$ and $\vec b$ be perpedicular to each other, and a unit vector $\vec c$ be inclined at an angle $\theta$ to both $\vec a$ and $\vec b$ . If $\vec c = \alpha \vec a + \beta \vec b + \gamma (\vec a \times \vec b)$ .

Precisely how many of the following equations are true?

**
(A)
**
:
$\alpha =\beta$
.

**
(B)
**
:
$1 - 2\alpha^2 = \gamma^2$
.

**
(C)
**
:
$\alpha^2 = \frac{1+\cos2\theta}2$
.

**
(D)
**
:
$\alpha^2 - \beta^2= \gamma^2$
.

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