# A semicircle is described on 'XY' as diameter and points A,B,C and D are chosen on arc 'XY' and quadrilateral ABCD is drawn.Then maximise tanA+tanB+tanC+tanD.

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by msnitish

I want procedure completely .

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by msnitish

I want procedure completely .

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so C+D=90 =90-D

for a quadrilateral

A+B+C+D=360

A+B=270

tan A + tan B + tan C + tan D=tan A + tan (270-A) + tan (90-D) + tan D

=tan A + cot A + cot D + tan D

so C+D=90 =>C=90-D

for a quadrilateral

A+B+C+D=360 =>A+B+90=360=>A+B=360-90

A+B=270

tan A + tan B + tan C + tan D=tan A + tan (270-A) + tan (90-D) + tan D

=tan A + cot A + cot D + tan D