已知2tanθ/1+tan^2θ=3/5,求sin^2(π/4+θ)
问题描述：
已知2tanθ/1+tan^2θ=3/5,求sin^2(π/4+θ)
答
2tanθ/1+tan^2θ=3/5
即tan2θ=3/5
sin2θ=3/根号(34)
cos2θ=5/根号(34)
sin^2(π/4+θ)
= (1-cos(2θ+π/2))/2
= (1+sin(2θ))/2
=( 1+3/根号(34))/2
=( 34+3根号(34))/68
现在对了么?
采吧.还是不对==那是多少？sin2θ=3/5（万能公式）2sinθcosθ=3/5sin^2(π/4+θ)=（根号2/2*cosθ+根号2/2*sinθ）^2=1/2(cosθ+sinθ)^2cos^2θ+2sinθcosθ+sin^θ=8/5(cosθ+sinθ)^2=8/5sin^2(π/4+θ)=4/5