sin(B/2)=cos(A+B/2) 则B/2+(A+B/2)=90——B+A/2=90 所以为等腰三角形sin(B/2)=cos(A+B/2)则B/2+(A+B/2)=90——B+A/2=90则C+A/2=90——B=C所以为等腰三角形没看明白第一步怎么到第二步的
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![sin(B/2)=cos(A+B/2) 则B/2+(A+B/2)=90——B+A/2=90 所以为等腰三角形sin(B/2)=cos(A+B/2)则B/2+(A+B/2)=90——B+A/2=90则C+A/2=90——B=C所以为等腰三角形没看明白第一步怎么到第二步的](/uploads/image/z/13563722-2-2.jpg?t=sin%28B%2F2%29%3Dcos%28A%2BB%2F2%29+%E5%88%99B%2F2%2B%28A%2BB%2F2%29%3D90%E2%80%94%E2%80%94B%2BA%2F2%3D90+%E6%89%80%E4%BB%A5%E4%B8%BA%E7%AD%89%E8%85%B0%E4%B8%89%E8%A7%92%E5%BD%A2sin%28B%2F2%29%3Dcos%28A%2BB%2F2%29%E5%88%99B%2F2%2B%28A%2BB%2F2%29%3D90%E2%80%94%E2%80%94B%2BA%2F2%3D90%E5%88%99C%2BA%2F2%3D90%E2%80%94%E2%80%94B%3DC%E6%89%80%E4%BB%A5%E4%B8%BA%E7%AD%89%E8%85%B0%E4%B8%89%E8%A7%92%E5%BD%A2%E6%B2%A1%E7%9C%8B%E6%98%8E%E7%99%BD%E7%AC%AC%E4%B8%80%E6%AD%A5%E6%80%8E%E4%B9%88%E5%88%B0%E7%AC%AC%E4%BA%8C%E6%AD%A5%E7%9A%84)
sin(B/2)=cos(A+B/2) 则B/2+(A+B/2)=90——B+A/2=90 所以为等腰三角形sin(B/2)=cos(A+B/2)则B/2+(A+B/2)=90——B+A/2=90则C+A/2=90——B=C所以为等腰三角形没看明白第一步怎么到第二步的
sin(B/2)=cos(A+B/2) 则B/2+(A+B/2)=90——B+A/2=90 所以为等腰三角形
sin(B/2)=cos(A+B/2)
则B/2+(A+B/2)=90——B+A/2=90
则C+A/2=90
——B=C
所以为等腰三角形
没看明白第一步怎么到第二步的
sin(B/2)=cos(A+B/2) 则B/2+(A+B/2)=90——B+A/2=90 所以为等腰三角形sin(B/2)=cos(A+B/2)则B/2+(A+B/2)=90——B+A/2=90则C+A/2=90——B=C所以为等腰三角形没看明白第一步怎么到第二步的
因为 (A+B)/2是锐角,所以π/2-(A+B)/2也是锐角,
sin(B/2)=cos(A+B/2)=sin(π/2-(A+B)/2)
由于 B/2与 π/2-(A+B)/2都是锐角,而sin在[0,π]上单调递增
所以B/2=π/2-(A+B)/2
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