Question

if (1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC)=k

Answer 1

(1-sinA)(1-sinB)(1-sinC)=(1+sinA)(1+sinB)(1+sinC)=k

this is possible only when

(1-sinA)=(1+sinA)
(1-sinB)=(1+sinB)
(1-sinC)=(1+sinC)

now,
(1-sinA)=(1+sinA)
sinA=0
A=0
in the same way B=C=0
now,
k=(1-0)(1-0)(1-0)=(1+0)(1+0)(1+0)=1 x 1 x 1=1
hence,
k=1