若tana加cota=4,则sin2a=?请解讲下 谢谢
若tana加cota=4,则sin2a=?
【万能公式推导：
因为sin2α=2sinαcosα=2sinα*[sinα/tanα]=2sin^2 α/tanα
又，sin^2 α+cos^2 α=1
===> 1+(cos^2 α/sin^2 α)=1/sin^2 α
===> 1+(1/tan^2 α)=1/sin^2 α
===> (1+tan^2 α)/tan^2 α=1/sin^2 α
===> sin^2 α=tan^2 α/(1+tan^2 α)
所以，sin2α=2sin^2 α/tanα=2[tan^2 α/(1+tan^2 α)]/tanα
=2tanα/(1+tan^...全部
若tana加cota=4,则sin2a=?
【万能公式推导：
因为sin2α=2sinαcosα=2sinα*[sinα/tanα]=2sin^2 α/tanα
又，sin^2 α+cos^2 α=1
===> 1+(cos^2 α/sin^2 α)=1/sin^2 α
===> 1+(1/tan^2 α)=1/sin^2 α
===> (1+tan^2 α)/tan^2 α=1/sin^2 α
===> sin^2 α=tan^2 α/(1+tan^2 α)
所以，sin2α=2sin^2 α/tanα=2[tan^2 α/(1+tan^2 α)]/tanα
=2tanα/(1+tan^2 α)
】
即，sin2α=2tanα/(1+tan^2 α)=2/(tanα+cotα)【分子分母同除以tanα】
=2/4
=1/2。
收起
