问答题(2021年天津市

在△ABC中,角A,B,C所对的边分别为a,b,c.已知sinA:sinB:sinC=2:1:√2,b=√2.

(1)求a的值;

(2)求cosC的值;

(3)求sin⁡(2C-π/6)的值.

答案解析

(1)由正弦定理得a:b=sinA:sinB=2:1,∵b=√2∴a=2√2.(2)同(1)可得c=2.由余弦定理得cosC=(a2+b2-c2)/2ab=((2√2)2+(√2)2-22)/(2×2√2×√2)=3/4.(3) cosC=3/4>0,则sinC==√7...

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