这几道数学题这么求啊(1)若cosα=1/7,α∈(0,π/2),则cos(α+π/3)=(2)化简cos(π/3+α)+sin(π/6+α)=(3)求值(1+cos20)/(2sin20)-sin10[(1/tan5)-tan5](4)已知α∈(0,π/2),tanα=1/2,求tan2α和sin(2α+π/3)的值(5)sin163sin223+sin253sin31
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![这几道数学题这么求啊(1)若cosα=1/7,α∈(0,π/2),则cos(α+π/3)=(2)化简cos(π/3+α)+sin(π/6+α)=(3)求值(1+cos20)/(2sin20)-sin10[(1/tan5)-tan5](4)已知α∈(0,π/2),tanα=1/2,求tan2α和sin(2α+π/3)的值(5)sin163sin223+sin253sin31](/uploads/image/z/10352135-47-5.jpg?t=%E8%BF%99%E5%87%A0%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%E8%BF%99%E4%B9%88%E6%B1%82%E5%95%8A%281%29%E8%8B%A5cos%CE%B1%3D1%2F7%2C%CE%B1%E2%88%88%280%2C%CF%80%2F2%29%2C%E5%88%99cos%28%CE%B1%2B%CF%80%2F3%29%3D%282%29%E5%8C%96%E7%AE%80cos%28%CF%80%2F3%2B%CE%B1%29%2Bsin%28%CF%80%2F6%2B%CE%B1%29%3D%283%29%E6%B1%82%E5%80%BC%281%2Bcos20%29%2F%282sin20%29-sin10%5B%281%2Ftan5%29-tan5%5D%284%29%E5%B7%B2%E7%9F%A5%CE%B1%E2%88%88%280%2C%CF%80%2F2%29%2Ctan%CE%B1%3D1%2F2%2C%E6%B1%82tan2%CE%B1%E5%92%8Csin%282%CE%B1%2B%CF%80%2F3%29%E7%9A%84%E5%80%BC%285%29sin163sin223%2Bsin253sin31)
这几道数学题这么求啊(1)若cosα=1/7,α∈(0,π/2),则cos(α+π/3)=(2)化简cos(π/3+α)+sin(π/6+α)=(3)求值(1+cos20)/(2sin20)-sin10[(1/tan5)-tan5](4)已知α∈(0,π/2),tanα=1/2,求tan2α和sin(2α+π/3)的值(5)sin163sin223+sin253sin31
这几道数学题这么求啊
(1)若cosα=1/7,α∈(0,π/2),则cos(α+π/3)=
(2)化简cos(π/3+α)+sin(π/6+α)=
(3)求值(1+cos20)/(2sin20)-sin10[(1/tan5)-tan5]
(4)已知α∈(0,π/2),tanα=1/2,求tan2α和sin(2α+π/3)的值
(5)sin163sin223+sin253sin313=
(6)已知α∈(π/2,π),tan(α+π/4)=1/7,则cosα=
下面这个展开后为什么得到(tana+1)/(1-tana))=1/7
(6)tan(α+π/4)=1/7展开(tana+1)/(1-tana))=1/7
解tana=-3/4推出sina=3/5,cosa=-4/5
这几道数学题这么求啊(1)若cosα=1/7,α∈(0,π/2),则cos(α+π/3)=(2)化简cos(π/3+α)+sin(π/6+α)=(3)求值(1+cos20)/(2sin20)-sin10[(1/tan5)-tan5](4)已知α∈(0,π/2),tanα=1/2,求tan2α和sin(2α+π/3)的值(5)sin163sin223+sin253sin31
(1)先求sina取正的再代入,自己带吧
(2)化简cos(π/3+α)+sin(π/6+α)=cos(π/3+α)+cos[π/2-(π/6+α)]
=cos(π/3+α)+cos(π/3-α)
=cosπ/3casα-sinαsinπ/3+cosπ/3casα+sinαsinπ/3
=2cosπ/3casα=casα
(3)[(1+cos20°)/2sin20°]-sin10°(1/tan5°-tan5°)
=[(1+cos20°)/2sin20°]-sin10°(cot5°-tan5°)
=[(1+cos20°)/4sin10°cos10°]-sin10°(cot5°-tan5°)
=(2cos10°/4sin10°)-2sin5°cos5°(cot5°-tan5°)
=(cos10°/2sin10°)-2((cos5°)^2-(sin5°)^2)
=(cos10°/2sin10°)-2cos10°
=(cos10°-4sin10°cos10°)/2sin10°
=(sin80°-2sin20°)/2sin10°
=((sin80°-sin20°)-sin20°)/2sin10°
=(2cos50°sin30°-sin20°)/2sin10°
=(sin40°-sin20°)/2sin10°
={2cos30°sin10°)/2sin10°
=cos30°
=(根号3)/2
(4)tan2α直接用公式,sina+根3分之一,cosa=根下(2/3)带入求sin(2α+π/3)
(5)sin163sin223+sin253sin313
=sin(180-17)sin(180+43)+sin(180+73)sin(360-47)
=-sin17sin43+sin73sin47
=-cos73sin43+sin73cos43
=sin(73-43)
=sin30
=1/2
(6)tan(α+π/4)=1/7展开(tana+1)/(1-tana))=1/7
解tana=-3/4推出sina=3/5,cosa=-4/5