已知tanα=2,求(sin^2α-2cos^2α)/(1+sin^2α)的值
问题描述：
已知tanα=2,求(sin^2α-2cos^2α)/(1+sin^2α)的值
答
(sin^2α-2cos^2α)/(1+sin^2α)
=[(sin²α-2cos²α)÷cos²α]/[(sin²α+cos²α+sin²α)÷cos²α]
=[tan²α-2]/[2tan²α+1]
=[2²-2]/[2×2²+1]
=2/9
答
tanα=2
(sinα)^2 = 2/5
(cosα)^2 = 1/5
((sinα)^2-2(cosα)^2)/(1+(sinα)^2)
=(2/5-2/5)/(1+2/5)
=0
答
(sin²α-2cos²α)/(1+sin²α)
=(sin²α-2cos²α)/(sin²α+cos²α+sin²α)
=(sin²α-2cos²α)/(2sin²α+cos²α)
=(tan²α-2)/(2tan²α+1) 【上式分子分母同时除以cos²α得到的】
=(2²-2)/(2×2²+1)
=2/9
答案：2/9