If θ is an angle between the two asymptotes of the hyperbola x2a2−y2b2=1, then cos⁡θ2 is equal to

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ba2+b2

aba2+b2

aa2+b2

a−ba+b

answer is C.

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Detailed Solution

Slopes of the asymptotes are ±ba⇒tan⁡θ=ba−−ba1+ba−ba⇒2tan⁡θ21−tan2⁡θ2=2(b/a)1−ba2⇒tan⁡θ2=ba as tan⁡θ2>0⇒cos⁡θ2=11+b2a2=aa2+b2

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