Question

△ABC角中,A,B,C的对边分别是abc,已知sinC+cosC=1-sinC/2

Answer 1

解： ∵sinC=2sin0.5C ×cos0.5C, cosC=cos0.5C×cos0.5C-sin0.5C×sin0.5C
∴2sin0.5C ×cos0.5C+cos0.5C×cos0.5C-sin0.5C×sin0.5C+sin0.5C=1
∵∠C<180°
∴sin0.5C,cos0.5C>0, 设sin0.5C=x
则有：2x×（1-x^2）^(1/2)+1-2×x^2+x=1
解得：x=[7^(1/2)-1]/4
∴cosC=cos0.5C×cos0.5C-sin0.5C×sin0.5C=1-2sin0.5C×sin0.5C
=1-2×x^2=7^(1/2)/4

又∵a^2+b^2=4(a+b)-8 化简得到：（a-2）^2+(b-2)^2=0
∴a=b=2

根据余弦定理：c^2 = a^2 + b^2 - 2·a·b·cosC
=4+4-8×7^(1/2)/4
∴c=7^(1/2)-1

追问

这个我也查过,有没有详细点的过程?

追答

这已经很详细啦，你哪里不懂了？