From the top of a cliff of height a, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height h. If θ be the angle of elevation then its value is:
A
cos−1√2ha
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B
sin−1√2ha
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C
sin−1√a2−h
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D
tan−1√3−2ha
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Solution
The correct option is Dtan−1√3−2ha h - a = x tan θ a = x tan 2θ (h - a)/a = tanθtan2θ=1−tan2θ2 (h/a) - 1 = 1−tan2θ2 (h/a) - 1 - 1/2 = tan2θ2 tan2θ = 3 - (2h/a) tan θ = √3−(2h/a) θ = tan−1√3−2ha