Question

已知tanθ=1/2,则sin2θ+sinθ^2= (高一数学)

Answer 1

(sinθ)^2+sin2θ
=[(sinθ)^2+2sinθcosθ]
=[(sinθ)^2+2sinθcosθ] /(sin^2 θ+cos^2θ) (上下同除以cos^2 θ)
=((tanθ)^2+2tanθ)/(1+tan^2 θ)
=(1/4+1)/(1+1/4)
=1

Answer 2

∵tanθ=1/2
∴sinθ=(cosθ)/2
∴sin2θ=2sinθcosθ=cos²θ
∴sin2θ+sin²θ=cos²θ+sin²θ=1

Answer 3

因为tanθ=1/2，所以sinθ/cosθ=1/2,既cosθ=2sinθ
又因为sinθ^2+cosθ^2=1,所以sinθ^2=1/5
sin2θ+sinθ^2=2sinθcosθ+sinθ^2=4sinθ^2+sinθ^2=5sinθ^2=1

Answer 4

=2sin@cos@+sin@^2
=(2sin@cos@+sin@^2)/(sin@^2+cos@^2)
=(2tan@+tan@^2)/(tan@^2+1)
=1