Question

if ABCD is a cyclic quadrilateral then cos (180 + A) + cos (180-B) +cos(180-C) + sin(90-D) with explanation ​

Answer 1

Answer:

0 or cos90

Step-by-step explanation:

cyclic quadrilateral==>opposite angles are supplementary

==>A+C=B+D=180

A+C=180==>A=180-C==>cosA=cos(180-C)==> cosA = - cosC

similarly cosB= - cosD

cos(180+A)+cos(180-B)+cos(180-C)-sin(90-D)

= - cosA - cosB - cosC - cosD

= - cosA + cosD + cosA - cosD

= 0

= cos90