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In a quadrilateral if sin(A+B)/2cos(A-B...

In a quadrilateral if `sin(A+B)/2cos(A-B)/2+sin(c+D)/2cos(c-D)/2=2,` then `cosA/2cosB/2+cosA/2cosc/2+cosA/2 cosD/2+cosB/2 cosC/2+cosB/2 cosD/2+cosC/2 cosD/2=`

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`2sin((A+B)/(2)).cos((A-B)/(2)) + 2sin((C+D)/(2)) cos((C-D)/2)=4`
`rArr sinA+sinB+sinC+sinD=4`
`therefore A=B=C=D=90^(@)`
`rArr sum cosA/2. cosB/2=6 . 1/sqrt(2) xx 1/sqrt(2)`
`=6 xx 1/2=3`
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