1.

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to:(a) 4 (b) 2 (c) 1 (d) 0

Answer»

(d) 0

In a cyclic quadrilateral, the sum of the opposite angles is 180°. 

⇒ A + C = 180° and B + D = 180° 

∴ cos A + cos B + cos C + cos D 

= cos A + cos B + cos (180° – C) + cos (180° – B) 

= cos A + cos B – cos A – cos B 

= 0.



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