if (1+sina)(1+sinb)(1+sinc) = (1-sina)(1-sinb)(1-sinc) then, 0

Question

if (1+sina)(1+sinb)(1+sinc) = (1-sina)(1-sinb)(1-sinc) then, 0<a,b,c<pi/2, then each side is equal to 

a) sina sinb sinc
b)cosa cosb cosc
c)tana tanb tanc
d)1

anonymous · Answer

If 0<a,b,c<pi/2 then all three factors on the left side are greater than 1 so their product is greater than 1. On the other side, the factors are on (0, 1) so their product is on (0, 1). Thus the left-hand side cannot be equal to the right-hand side.

anonymous · Answer

However, if we allow the angles to be 0, then each side is 1.

anonymous · Answer

Which, coincidentally, is equal to (cosa cosb cosc).

anonymous · Answer

Thank you :)

anonymous · Answer

no problem:)