△ABC的内角A,B,C的对边分别为a,b,c.已知A—C=90°,a+c=根号2,求C解析:sinA+sinC=√2 sinB sin(90+C)+sinC=√2 sin(180-C-90-C)sinC+cosC=√2 cos2Csin(C+45)=sin(90-2C)C=15请问其中的B 有什么用处,sin(90+C)+sinC=√2 sin(180-C-90
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![△ABC的内角A,B,C的对边分别为a,b,c.已知A—C=90°,a+c=根号2,求C解析:sinA+sinC=√2 sinB sin(90+C)+sinC=√2 sin(180-C-90-C)sinC+cosC=√2 cos2Csin(C+45)=sin(90-2C)C=15请问其中的B 有什么用处,sin(90+C)+sinC=√2 sin(180-C-90](/uploads/image/z/3740677-61-7.jpg?t=%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc.%E5%B7%B2%E7%9F%A5A%E2%80%94C%3D90%C2%B0%2Ca%2Bc%3D%E6%A0%B9%E5%8F%B72%2C%E6%B1%82C%E8%A7%A3%E6%9E%90%EF%BC%9AsinA%2BsinC%3D%E2%88%9A2+sinB+sin%2890%2BC%29%2BsinC%3D%E2%88%9A2+sin%28180-C-90-C%29sinC%2BcosC%3D%E2%88%9A2+cos2Csin%28C%2B45%29%3Dsin%2890-2C%29C%3D15%E8%AF%B7%E9%97%AE%E5%85%B6%E4%B8%AD%E7%9A%84B+%E6%9C%89%E4%BB%80%E4%B9%88%E7%94%A8%E5%A4%84%2Csin%2890%2BC%29%2BsinC%3D%E2%88%9A2+sin%28180-C-90)
△ABC的内角A,B,C的对边分别为a,b,c.已知A—C=90°,a+c=根号2,求C解析:sinA+sinC=√2 sinB sin(90+C)+sinC=√2 sin(180-C-90-C)sinC+cosC=√2 cos2Csin(C+45)=sin(90-2C)C=15请问其中的B 有什么用处,sin(90+C)+sinC=√2 sin(180-C-90
△ABC的内角A,B,C的对边分别为a,b,c.已知A—C=90°,a+c=根号2,求C
解析:sinA+sinC=√2 sinB
sin(90+C)+sinC=√2 sin(180-C-90-C)
sinC+cosC=√2 cos2C
sin(C+45)=sin(90-2C)
C=15
请问其中的B 有什么用处,sin(90+C)+sinC=√2 sin(180-C-90-C)和sin(C+45)=sin(90-2C)这步又是怎么得到的
下面的答案都是牛头不对马嘴
△ABC的内角A,B,C的对边分别为a,b,c.已知A—C=90°,a+c=根号2,求C解析:sinA+sinC=√2 sinB sin(90+C)+sinC=√2 sin(180-C-90-C)sinC+cosC=√2 cos2Csin(C+45)=sin(90-2C)C=15请问其中的B 有什么用处,sin(90+C)+sinC=√2 sin(180-C-90
题目打漏了,a+c=根号2应该是a+c=√2b
第一步的B是由原题转化过来,然后再转变成C的方程求解
第一步是由正弦定理a=bsin A÷sin B c=bsin C÷sin B代入原式得到的
第二步是由A-C=90得A=90+C,B=180-C-A=180-C-90-C
第四步是由第三步sinC+cosC=√2 cos2C →√2/2sinC+√2/2cosC=cos2C
→cos 45sinC+sin 45cosC=cos2C=sin(90-2C)
→sin(C+45)=sin(90-2C)
哪里不懂问啊,已经讲得很详细了
题目错了!! △ABC内角A、B、C的对边分别为a、b、c,已知A-C=90°,a+c=根号2b,求∠c 因为a+c=根号2b。 所以 sinA+sinC=根号2sinB, sin(90+C)+sinC=根号2sin(A+C), cosC+sinC=根号2sin(90+2C), cosC+sinC=根号2cos2C, cosC+sinC=根号2(cos^2C-sin^2C) cosC+sinC=根号2(cosC+sinC)( cosC-sin C) 由已知C是锐角,所以根号2( cosC-sinC) =1, 2cos (C+45) =1, C+45=60, C=15
三角公式啊