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If θ is the angle between unit vectors $large vec A$ and $large vec B$ then $large frac{{(1 - vec A.vec B)}}{{(1 + vec A.vec B)}}$ is equal to

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tan² ( θ / 2)

sin² (θ / 2)

cot² (θ/2)

cos² (θ/2)

answer is A.

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Detailed Solution

$frac{{1 - vec A.vec B}}{{1 + vec A.vec B}} = frac{{1 - ABcos theta }}{{1 + ABcos theta }};;(A = 1,;B = 1)$

$frac{{1 - cos theta }}{{1 + cos theta }} = frac{{2{{sin }^2}theta /2}}{{2{{cos }^2}theta /2}} = {tan ^2}theta /2$

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