若3sinθ=cosθ,则cos2θ+sin2θ的值等于

问题描述:

若3sinθ=cosθ,则cos2θ+sin2θ的值等于

3sinθ=cosθ
所以tanθ=1/3
cos2θ+sin2θ
=(cos²θ-sin²θ+2sinθcosθ)/(sin²θ+cos²θ)
=(1-tan²θ+2tanθ)/(tan²θ+1)
=7/5