tanθ=sinθ/cosθ=2
sinθ=2cosθ
sin²θ+cos²θ=1
(2cosθ)²+cos²θ=1
5cos²θ=1
cos²θ=1/5
sin²θ+sin2θ
=(2cosθ)+2sinθcosθ
=4cos²θ+2(2cosθ)cosθ
=4cos²θ+4cos²θ
=8cos²θ
=8×(1/5)
=8/5
或者这样
tanθ=2
sin²θ+2sinθcosθ
=(sin²θ+2sinθcosθ)/(sin²θ+cos²θ)
=(tan²θ+2tanθ)/(tan²θ+1)
=(2²+2×2)/(2²+1)
=8/5
两种方法结果是一样的.