A cone of semi-vertical angle a is inscribed in
a sphere of radium 2 cm. The height of the cone
is
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Al = OL = 2(radius of the sphere)
Angle ALM = 2a(exterior angle of the triangle is the same as sum of the interior opposite angles)
Therefore, LM = OL cos 2a = 2 cos 2a
height of the cone
= OM = OL + LM = 2 + 2 cos a
= 2(1 + cos2a)
= 2 × 2 cos² a =
= 4 cos² a
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