sinx+cosx
=√2sin(x+π/4)
(1)當(dāng)x∈[0,π]
x+π/4∈[π/4,5π/4]
√2sin(x+π/4)∈[-1,√2]
有且只有一個(gè)解
從圖像得
2m∈[-1,1)
m∈[-1/2,1/2)
（2）當(dāng)x∈R
√2sin(x+π/4)∈[-√2,√2]
2m∈[-√2,√2]
m∈[-√2/2,√2/2]
（3）x∈[0,2π]
x+π/4∈[π/4,9π/4]
√2sin(x+π/4)∈[-√2,√2]
有兩解α,β
1<2m<√2,-√2<2m<1
2m=√2,-√2時(shí)有1根
2m=1時(shí)有3根
1/2α+π/4+β+π/4=π/2或3π/2
α+π/4,β+π/4關(guān)于x=π/2或3π/2對(duì)稱
α+β=0或π
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