赞 joe101010 幼苗
共回答了12个问题采纳率：91.7% 举报
已知sin(a)+sin(b)=0.5^0.5
所以,
[sin(a)+sin(b)]^2
=sin^2(a)+sin^2(b)+2sin(a)sin(b)
=0.5
[cos(a)+cos(b)]^2
=cos^2(a)+cos^2(b)+2cos(a)cos(b)
两式相加得到
0.5+[cos(a)+cos(b)]^2
=sin^2(a)+sin^2(b)+2sin(a)sin(b)+cos^2(a)+cos^2(b)+2cos(a)cos(b)
=2+2cos(a-b)
∈[0,4]
所以,[cos(a)+cos(b)]^2∈[0,7/2]
而cos(a)+cos(b)≤√2
cos(a)+cos(b)∈[0,√2]
所以,
[sin(a)+sin(b)]^2
=sin^2(a)+sin^2(b)+2sin(a)sin(b)
=0.5
[cos(a)+cos(b)]^2
=cos^2(a)+cos^2(b)+2cos(a)cos(b)
两式相加得到
0.5+[cos(a)+cos(b)]^2
=sin^2(a)+sin^2(b)+2sin(a)sin(b)+cos^2(a)+cos^2(b)+2cos(a)cos(b)
=2+2cos(a-b)
∈[0,4]
所以,[cos(a)+cos(b)]^2∈[0,7/2]
而cos(a)+cos(b)≤√2
cos(a)+cos(b)∈[0,√2]
1年前
4
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