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Given is A+B+C=0 then what is the value of sinA+sinB+sinC= a)-2sinA/2 sinB/2 sinC/2 b)-4sinA/2 sinB/2 sinC/2

Given is A+B+C=0 then what is the value of sinA+sinB+sinC=
 
a)-2sinA/2 sinB/2 sinC/2
b)-4sinA/2 sinB/2 sinC/2

Grade:11

1 Answers

Susmita
425 Points
5 years ago
A+B+C=0
Or,A=-(B+C)
sinA+sinB+sinC
=-sin(B+C)+sinB+sinC
=-sinBcosC-sinCcosB+sinB+sinC
=sinB(1-cosC)+sinC(1-cosB)
=sinB.2sin2(C/2)+sinC.2sin2(B/2)
=2sin(B/2)cos(B/2).2sin2(C/2)+2sin(C/2)cos(C/2l.2sin2(B/2)
=4sin(B/2)sin(C/2)[cos(B/2)sin(C/2)+cos(C/2)sin(B/2)]
=4sin(B/2)sin(C/2)sin{(B+C)/2}
=-4sin(B/2)sin(C/2)sin(A/2)
If it helps please approve.
 

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