tan(a+π/4)=k,则cos2a=?
问题描述：
tan(a+π/4)=k,则cos2a=?
答
tan(a+π/4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(tana+1)/(1-tana)
=k
∴tana=(k-1)/(k+1)
cos2a
=cos²a-sin²a
=(cos²a-sin²a)/1
=(cos²a-sin²a)/(cos²a+sin²a)
分子分母同除cos²a得
=(1-tan²a)/(1+tan²a)
=(2k)/(k²+1)
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