若tanθ=1/3,则cos²θ+1/2sin2θ的值

若tanθ=1/3,则cos²θ+1/2sin2θ的值
若tanθ=1/3,则cos²θ+1/2sin2θ的值

若tanθ=1/3,则cos²θ+1/2sin2θ的值
答：
tanθ=1/3
cos²θ+(1/2)sin2θ
=(cos²θ+sinθcosθ) / (sin²θ+cos²θ) 分子分母同除以cos²θ
=(1+tanθ) / (tan²θ+1)
=(1+1/3) /(1/9+1)
=(4/3) /(10/9)
=6/5

cos²θ+1/2sin2θ=6/5

过程：
cos²θ+1/2sin2θ
=cos²θ+sinθcosθ
=(cos²θ+sinθcosθ)/(sin²θ+cos²θ) [原理：sin²θ+cos²θ=1]
=(1+tanθ)/(tan²θ+1)...

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cos²θ+1/2sin2θ=6/5

过程：
cos²θ+1/2sin2θ
=cos²θ+sinθcosθ
=(cos²θ+sinθcosθ)/(sin²θ+cos²θ) [原理：sin²θ+cos²θ=1]
=(1+tanθ)/(tan²θ+1) [分子分母同除以cos²θ]
=(1+1/3)/(1/9+1)
=(4/3)/(10/9)
=6/5

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