Question

if cosx+cosy=a,sinx+siny=b,then sin(x+y)=​

Answer 1

Answer:

The teacher asked me to do it show

Answer 2

Answer:

2ab/(a^2 +b^2)

Step-by-step explanation:

Sinx + siny = a ; Cosx + cosy = b. What is the value of cos(x+y) and sin(x+y)?

*A2A

⟹sinx+siny=a

⟹2sin((x+y)/2)cos((x−y)/2)=a⋯(1)

⟹cosx+cosy=b

⟹2cos((x+y)/2)cos((x−y)/2)=b⋯(2)

⋆ Dividing (1) by (2) we get :-

⟹tan((x+y)/2)=ab

⋆ Now,

⟹sin(x+y)=2tan((x+y)/2)/(1+tan2((x+y)/2))

⟹sin(x+y)=2ab/(a2+b2)