cos[alpha]+cos[beta]+cos[gamma]=3. Find the value of sin[alpha]+sin[beta]+sin[gamma].

cos[alpha]+cos[beta]+cos[gamma]=3  -------1

this can only be possible when cos[alpha] ,cos [beta] ,cos [gamma]     are all equal to 1

for no other value of cos[alpha] ,cos [beta] ,cos [gamma]  the equation 1 holds true as max value of cosine is 1.

the values of alpha , beta , gamma are all 2npie  where n is any integer and for this value

so sin[alpha] = sin[beta] = sin [gamma] =0

so their sum is also 0     

so answer is 0