Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle points of B and Q, which are feet of these two poles. Let $\frac{\pi }{8}$  and q be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan²q is equal to

Correct Option - 3


Detailed Solution:

$tan\frac{\pi }{8}=\frac{2h}{80}.........(i)$

$tan\theta =\frac{h}{80}..........(ii)$

$\Rightarrow tan\frac{\pi }{8}=2tan\theta$

$ta{n}^2\theta =\frac{3-2\sqrt[]{2}}{4}$

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