已知tan35度=a,则cos20度(1-sin20度)=

Question

已知tan35度=a,则cos20度(1-sin20度)=

Answer 1

cos20°(1-sin20°)
=sin70°(1-cos70°)
=2sin35°cos35°*2(sin35°)^2
=4(sin35°)^3cos35°
=4(sin35°)^3cos35°/[(sin35°)^2+(cos35°)^2]^2 (添上分母1,并转化）
=4(tan35°)^3/[(tan35°)^2+1]^2 (分子分母同除以 (cos35°)^2 )
=4a^3/(a^2+1)^2 .