Question

若α≠0,且sinx+cosy=α,cosx+cosy=α,则sinx+cosx=

Answer 1

sinx+cosy=α,------(1)

cosx+cosy=α-------(2)

(1)-(2)

sinx-cosx=0 ,1-2sinxcosx=0 ,2sinxcosx=1

(sinx+cosx)^2=1+ 2sinxcosx=2

sinx+cosx=±√2

sinx+siny=a,cosx+cosy=a

sin²y=(a-sinx)²=a²-2asinx+sin²x,---(1)

cos²y=a²-2acosx+cos²x---------------(2)

(1)+(2)

1=2a²-2asinx-2acosx+1 0=2a²-2a(sinx+cosx)

sinx+cosx=a