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In quadrilateral A B C D , if sin((A+B)/...

In quadrilateral `A B C D ,` if `sin((A+B)/2)cos((A-B)/2)+"sin"((C+D)/2)cos((C-D)/2)=2` then find the value of `sinA/2sinB/2sinC/2sinD/2dot`

Text Solution

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`sin((A+B)/(2))cos((A-B)/(2))+sin((C+D)/(2))cos((C-D)/(2))`
=2
or `(1)/(2)[sinA+sinB+sinC+sinD]=2`
or `sinA+sinB+sinC+sinD=4`
`rArr A=B=C=D=90^(@)`
`rArr sin""(A)/(2)sin""(B)/(2)sin""(C)/(2)sin""(D)/(2)=(1)/(4)`
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