问题
填空题
已知tanθ=2,则sin2θ+2sinθcosθ-2cos2θ=______.
答案
∵tanθ=2,
∴sin2θ+2sinθcosθ-2cos2θ
=sin 2θ+2sinθcosθ-2cos 2θ cos2θ+sin2θ
=
=tan 2θ+2tanθ-2 1+tan 2θ
=4+4-2 1+4
.6 5
故答案为:6 5
已知tanθ=2,则sin2θ+2sinθcosθ-2cos2θ=______.
∵tanθ=2,
∴sin2θ+2sinθcosθ-2cos2θ
=sin 2θ+2sinθcosθ-2cos 2θ cos2θ+sin2θ
=
=tan 2θ+2tanθ-2 1+tan 2θ
=4+4-2 1+4
.6 5
故答案为:6 5