三角形ABC中,根号2sinC/2的平方+cosC/2,求角C,若abc乘等比数列求sinA根号2乘sin^2C/2+cosC/2=根号2
问题描述：
三角形ABC中,根号2sinC/2的平方+cosC/2,求角C,若abc乘等比数列求sinA
根号2乘sin^2C/2+cosC/2=根号2
答
1)√2sin^2C/2+cosC/2=√2(1-cos^2C/2)+cosC/2=√2
即cosC/2-√2cos^2C/2=0
cosC/2=0或√2/2
C∈(0,π) C/2∈(0,π/2)
C/2=π/4 C=π/2
2)abc成等比数列
b^2=ac
sin^2B=sinAsinC=sin^2(A+C)
即sinA=cos^2A=1-sin^2A
sinA=(-1+√5)/2