已知tanα=1/2,则((1/4)sin^2)
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已知tanα=1/2,则((1/4)sin^2)
((1/4)sin^2A+(3/4)cos^2A)/(sin^2A-cos^2A)
((1/4)sin^2A+(3/4)cos^2A)/(sin^2A-cos^2A)
[(1/4)sin^2A+(3/4)cos^2A]/(sin^2A-cos^2A)分子分母同时除以cos^2A
=[(1/4)sin^2A/cos^2A+(3/4)cos^2A/cos^2A]/(sin^2A/cos^2A-cos^2A/cos^2A)
=[(1/4)tan^2A+3/4]/(tan^2A-1)
=[(1/4)*(1/2)^2+3/4]/[(1/2)^2-1]
=[1/4*1/4+3/4]/[1/4-1]
=[1/4*1/4+3/4]/[-3/4]
=[1/4+3]/(-3)
=(13/4)/(-3)
=-13/12
=[(1/4)sin^2A/cos^2A+(3/4)cos^2A/cos^2A]/(sin^2A/cos^2A-cos^2A/cos^2A)
=[(1/4)tan^2A+3/4]/(tan^2A-1)
=[(1/4)*(1/2)^2+3/4]/[(1/2)^2-1]
=[1/4*1/4+3/4]/[1/4-1]
=[1/4*1/4+3/4]/[-3/4]
=[1/4+3]/(-3)
=(13/4)/(-3)
=-13/12
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