已知向量a=(1-cosθ,√2),b=(sinθ,1),且a//b,则tanθ/2的值为
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![已知向量a=(1-cosθ,√2),b=(sinθ,1),且a//b,则tanθ/2的值为](/uploads/image/z/5192642-2-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%EF%BC%881-cos%CE%B8%2C%E2%88%9A2%EF%BC%89%2Cb%3D%EF%BC%88sin%CE%B8%2C1%EF%BC%89%2C%E4%B8%94a%2F%2Fb%2C%E5%88%99tan%CE%B8%2F2%E7%9A%84%E5%80%BC%E4%B8%BA)
已知向量a=(1-cosθ,√2),b=(sinθ,1),且a//b,则tanθ/2的值为
已知向量a=(1-cosθ,√2),b=(sinθ,1),且a//b,则tanθ/2的值为
已知向量a=(1-cosθ,√2),b=(sinθ,1),且a//b,则tanθ/2的值为
a∥b,即:(1-cosθ)/sinθ=√2
令:t=tan(θ/2)
sinθ=2t/(1+t^2)
cosθ=(1-t^2)/(1+t^2)
即:1-cosθ=2t^2/(1+t^2)
即:2t^2/(1+t^2)/(2t/(1+t^2))=t=√2
即:tan(θ/2)=√2
1-cosθ/√2=sinθ/1
-0.5=sina/cosa
tana=-0.5