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If A,B,C,D are the four angles taken in ...

If A,B,C,D are the four angles taken in order of a cyclic quadrilateral prove that (i)`tanA +tanB+tanC+tanD=0` (ii)`cos(180^@-A)+cos(180^@+B)+cos(180-C^@)-sin(90+D)=0` (iii)`cosA+cosB+cosC+cosD=0` (iv)`tan(A+B)+tan(C+D)=0`

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