Question

Sinx +siny =-21/65 and cosx +cosy =-27/65 then cos(x+y/2

Answer 1

Answer:

27/√1170

Step-by-step explanation:

Sinx + Siny = - 21/65

Cosx + Cosy = - 27/65

Divide them,

Sinx + Siny/Cosx + Cosy = 21/27

2Sinx+y/2)Cos(x-y/2) / 2Cos(x+y/2)Cos(x-y/2) = 21/27

Tan(x+y/2) = 21/27

Cos(x+y/2) = 1/√ 1 + Tan²(x+y/2)  (∵ Sec²x = 1 + Tan²x => Cosx = 1/√1 + tan²x)

                  = 1/√ 1 + (21/27)²

                   = 27 /√ (27)² + (21)²

                     = 27 / √729 + 441

                     = 27/√1170