f(tanx)=1+sin²x,则f(cos60°)=?急.我数学不好,明天期末考了,

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f(tanx)=1+sin²x,则f(cos60°)=?急.我数学不好,明天期末考了,
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f(tanx)=1+sin²x,则f(cos60°)=?急.我数学不好,明天期末考了,
f(tanx)=1+sin²x,则f(cos60°)=?
急.我数学不好,明天期末考了,

f(tanx)=1+sin²x,则f(cos60°)=?急.我数学不好,明天期末考了,
cos60°=1/2
tanx=1/2时,根据勾股定理得sinx=根号5,sin²x=5
f(cos60°)=f(1/2)=1+5=6

f(tanx)=1+sin²x
=2-cos²x
=2-[(cos2x+1)/2]
=2-cos2x/2-1/2
=3/2-cos2x/2
=3/2-[(1-tan^x)/(1+tan^x)]/2
f(cos60°)
=3/2-[(1-cos^60°)/(1+cos^60°)]/2
=3/2-[(1-1/4)/2(1+1/4)]
=3/2-(3/4)/[2*5/4]
=3/2-(3/4)/[5/2]
=3/2-3/4*2/5
=3/2-3/10
=12/10
=6/5