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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`

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`1/2[2sin((A+B)/2)cos((A-B)/2)+2sin((C+D)/2)cos((C-D)/2)]=2`
`2sinCcosD=sin(C+D)+sin(C-D)`
`sinA+sinB+sinC+sinD=4`
`sinA-11=sinB=sinC=sinD`
`A=pi/2=B=C=D`
`sin(A/2)sin(B/2)sin(C/2)sin(D/2)`
`=sin^4pi/4=(1/sqrt2)^4=1/4`.
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Knowledge Check

  • Statement:1 If cos(A+B)sin( C +D) = cos(A-B) sin(C-D) , then the values of cotAcotBcotC is cotD. And Statement:2: If cos(A+B) sin(C+D)= cos(A-B) sin(C-D) then the value of tanAtanBtanC is tanD.

    A
    Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement-4
    B
    Statement-1 is true, Statement-2 is true, Statement-2 is not a correct expanation for statement-4
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    Statement-1 is True, Statement-2 is false
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    Statement-1 is False, Statement-2 is true

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