Question

已知sinA+cosA=2sina,sinA*cosA=(sinb)^2,求证4(cos2a)^2=(cos2b)^2

Answer 1

sinA^2+cosA^2=(sinA+cosA)^2-2sinA*cosA=1

(2sina)^2-2(sinb)^2=1

4sina^2-2sinb^2=1

2(1-cos2a)+cos2b-1=1

2cos2a=cos2b

即4(cos2a)^2=(cos2b)^2