已知tanθ=2,求sin²θ+2sinθ*cosθ+1的值

题目

已知tanθ=2,求sin²θ+2sinθ*cosθ+1的值

答案

tanθ=2
sin²θ+2sinθ*cosθ+1
= (sin²θ+2sinθ*cosθ)/1 + 1
= (sin²θ+2sinθ*cosθ)/(sin²θ+cos²θ) + 1
前边分子分母分别除以cos²θ：
= (tan²θ+2tanθ)/(tan²θ+1) + 1
= (2²+2×2)/(2²+1) + 1
= 13/5