cosC+√2 sinC=√3 ,与cos^2C+sin^2C=1联立 sinC= √6/3 求两式联立祥解过程,我怎么带都求不出啊

cosC+√2 sinC=√3 ,与cos^2C+sin^2C=1联立 sinC= √6/3 求两式联立祥解过程,我怎么带都求不出啊
cosC+√2 sinC=√3 ,与cos^2C+sin^2C=1联立 sinC= √6/3 求两式联立祥解过程,我怎么带都求不出啊

cosC+√2 sinC=√3 ,与cos^2C+sin^2C=1联立 sinC= √6/3 求两式联立祥解过程,我怎么带都求不出啊
∵cosC+√2sinC=√3
∴cosC=√3-√2sinC
又cos²C+sin²C=1
∴(√3-√2sinC)²+sin²C=1
即3sin²C-2√6sinC+2=0
则(√3sinC-√2)²=0
故√3sinC=√2
∴sinC=√2/√3=√6/3