Question

if sin x + sin y+ sin z =3 then find the value of cos x+ cos y+ cos z.

Answer 1

we know according to sine value
sin maximum value is 1 and minimum value is -1
hence
sinx €[-1,1]-----(1)
siny €[-1,1]-------(2)
sinz €[-1,1]-------(3)

here € means belongs to
know add all equation (1) , (2) and (3)

sinx+siny+sinz €[-3,3]
here we see
question given
sinx+siny+sinz=3
it means all sine value gain maximum then this is possible ,but we also know sine gain maximum value only on pi/2
hence x=y=z=pi/2

now
cosx+cosy+cosz=cos(pi/2)+cos (pi/2)+cos (pi/2)=0+0+0=0