已知tan(π/4 +α)=1/2.(1)求tanα的值;(2)求(sin2α-cos^α)/(1+cos2α)的值.
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已知tan(π/4 +α)=1/2.(1)求tanα的值;(2)求(sin2α-cos^α)/(1+cos2α)的值.
已知tan(π/4 +α)=1/2.
(1)求tanα的值;
(2)求(sin2α-cos^α)/(1+cos2α)的值.
已知tan(π/4 +α)=1/2.(1)求tanα的值;(2)求(sin2α-cos^α)/(1+cos2α)的值.
(1)
tan(π/4 +α)=1/2
[tan(π/4) +tanα]/[1-tan(π/4)tanα] =1/2
(1 +tanα)/(1-tanα) =1/2
2(1 +tanα)=1-tanα
3tanα = -1
tanα =-1/3
(2)
(sin2α-(cosα)^2)/(1+cos2α)
=(2sinαcosα-(cosα)^2)/(2(cosα)^2)
=(2tanα-1)/2
= ( -2/3-1)/2
= - 5/6
(1)tan(π/4+a)=(1+tana)/(1-tana)=1/2
tana=-1/3
(2)原式=(2sinacosa-cosa)/[1+(cosa)^2-(sina)^2]
=(2sinacosa-cosa)/2(cosa)^2
=(2sina-1)/2cosa
=tana-1/2cosa
cosa=3√10/10
原式=-1/3-√10/6
=-(√10+2)/6
tan(π/4+α)=(tanπ/4+tanα)/1-tanπ/4tanα=1/2
解得tanα=-1/3
(2)把sin2α换成2sinαcosα,把cos2α换成1-sin²α,然后分子分母同时除以cos²α,得出一个tan的式子,把tanα的得数带进去就可以算了
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