Question

已知sinθ 和cosθ的等差中项为sina 等比中项为sinb 则cos2a-1/2cos2b的值

Answer 1

sinθ 和cosθ的等差中项为sina ,等比中项为sinb,

∴sina=(sinθ+cosθ)/2,(sinb)^2=sinθcosθ,

∴cos2a=1-2(sina)^2=1-(1+2sinθcosθ)/2=(1-2sinθcosθ)/2,

cos2b=1-2(sinb)^2=1-2sinθcosθ,

∴cos2a-(1/2)cos2b=0.