分类：教育/科学-学习帮助
问题：在三角形ABC中求证三角形ABC中,若A:B:C=4:2:1,则 
求证三角形AB中,若A:B:C=4:2:1,则(1/a)+(1/b)=1/c
回答：三角形ABC中，A:B:C=4:2:1，则：A=4π/7，B=2π/7，C=π/7
由正弦定理：a/sinA = b/sinB = c/sinC = 2R
==> 1/a + 1/b =(1/2R)*(1/sinA +1/sinB)
= (1/2R)*[1/sin(4π/7) + 1/sin(2π/7)]
= (1/2R)*[sin(4π/7) +sin(2π/7)]/[sin(4π/7)sin(2π/7)]
= (1/2R)*[2*sin(3π/7)*cos(π/7)]/[sin(π-4π/7)*2*sin(π/7)cos(π/7)]
= (1/2R)*[1/sin(π/7)]
= 1/c