证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 19:10:33
证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC

证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC
证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)
证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC=1+2cos(B/2+C/2)[2sin(B/2)sin(C/2)] -cos(B+C)+cosB+cosC=1+2cos(B/2+C/2)[2sin(B/2)sin(C/2)] -cos(B+C)+cosB+cosC=1+2cos(B/2+C/2)[cos(B/2-C/2)-cos(B/2+C/2)] -cos(B+C)+cosB+cosC=1+2cos(B/2+C/2)cos(B/2-C/2)-2[cos(B/2+C/2)]^2 cosB+cosC=2cos(B/2+C/2)cos(B/2-C/2)

证明cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)证明：cosA＋cosB＋cosC=1+4sin(A/2)sin(B/2)sin(C/2)尽量详细一点选做cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2) cos(180-B-C)+cosB+cosC=1+2sin(A/2)[2sin(B/2)sin(C/2)] cos(180-B-C)+cosB+cosC
应该是在三角形中吧 ,要不然没法算
cosA+cosB+cosC
=2cos[(A+B)/2]cos[(A-B)/2]+cosC
=2cos[(π-C)/2]cos[(A-B)/2]+cosC
=2sin(c/2)cos[(A-B)/2]+1-2[sin(C/2)]^2
=1+2sin(c/2){cos[(A-B)/2]-[sin(C/2)]}
=1+2sin(c/2){cos[(A-B)/2]-[sin(π -A-B)/2]}
=1+2sin(c/2){cos[(A-B)/2]-[cos[(A+B)/2]}
=1+2sin(c/2)[-2sin(A/2)sin(-B/2)]
=1+4sin(A/2)sin(B/2)sin(C/2)

汗 愁啊 不懂

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