Question

sin^4+cos^4=1,求sin+cos=

Answer 1

（sinx）^4+（cosx）^4=1
即(sinx)^4+(cosx)^4+2(sinx)^2(cosx)^2-2(sinx)^2(cosx)^2=1
即[(sinx)^2+(cosx)^2]^2-2(sinxcosx)^2=1
即1-2(sinxcosx)^2=1
所以sinxcosx=0
所以sinx=0或cosx=0
当sinx=0时cosx=1或-1，
当sinx=0时cosx=1或-1
所以sinx+cosx=1或 -1

Answer 2

解:sin^4+cos^4=1
(sin^2+cos^2)^2-2sin^2cos^2=1
1-2sin^2cos^2=1
sin^2cos^2=0
sincos=0
(sin+cos)^2=sin^2+cos^2+2sincos=1+0=1
所以sin+cos=±1