Points A,B,C and D are chosen on a semicircle and quadrilateral ABCD is drawn.

Then tan A + tan B + tan C + tan D is

∞

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Solution

The correct option is D
0

1.A,B,C,D lie on the circumference of a semi circle i.e on a circle. ∴ ABCD is a cyclic quadrilateral.

Hence sum of opposite angle is π, i.e., C = π - A, D = π - B.

tan A + tan B + tan C + tan D

= tan A + tan B + tan(π - A)+tan( π - B) = 0

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