Question

在三角形ABC中,角A B C所对的边分别是a.b.c设函数fx=sinx（sinx+cosx）-1/2,且满足f（A）

Answer 1

f(x)=sinx(sinx+cosx)-1/2

=1/2(2sin²x-1+2sinxcosx)

=1/2(sin2x-cos2x)

=√2/2sin(2x-π/4)

2kπ-π/2≤2x-π/4≤2kπ+π/2

kπ-π/8≤x≤kπ+3π/8

2kπ+π/2≤2x-π/4≤2kπ+3π/2

kπ+3π/8≤x≤kπ+7π/8

因此,单增区间[kπ-π/8,kπ+3π/8];单减区间[kπ+3π/8,kπ+7π/8]

√2/2sin(2A-π/4)=1/2

A=π/2