半角的正切公式证明 tanx/2=sinx/1+cosx=1-cosx/sinx
问题描述:
半角的正切公式证明 tanx/2=sinx/1+cosx=1-cosx/sinx
答
tanx/2=(sinx/2)/(cosx/2)=(2sinx/2cosx/2)/2(cosx/2)^2=sinx/(1+cosx)
tanx/2=(sinx/2)/(cosx/2)=2(sinx/2)^2/(2sinxcosx/2)=(1-cosx)/sinx
答
证明:tan(x/2)=sin(x/2)/cos(x/2)
=2sin(x/2)cos(x/2)/[cos(x/2)]^2
=sinx/(1+cosx)
=sinx(1-cosx)/[1-(cosx)^2]
=sinx(1-cosx)/(sinx)^2
=(1-cosx)/sinx