InterviewSolution
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InterviewSolution
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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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Answer» `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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