Question

已知tan(a+派／4)＝2,则cos2a=

Answer 1

tan(a+π／4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(tana+1)/(1-tana)
=2
即1+tana=2(1-tana)
解得：tana=1/3
则sina=±√10/10
cos2a=1-2sin²a=1-2*(±√10/10)²=4/5

Answer 2

解：tan(α+π/4)=(tanα+tanπ/4)/(1-tanα*tanπ/4)=2.
tanα+1=2(1-tanα).
3tanα=1.
tanα=1/3.
cos2α=2cos^2α-1.
sec^2α= 1+tan^2α=1+(1/3)^2.
=10/9.
cos^2α=1/sec^2α=9/10.
cos2α=(2*9/10)-1.
cos2α=9/5-1.
∴ cos2α=4/5.

Answer 3

tan(a+派／4)＝2
（tana+1）/（1-tanatan派/4）=2
tana=1/3
cos2a=cosa^2-sina^2变形为
cos2a=（cosa^2-sina^2）/（cosa^2+sina^2）分子分母同时除以cosa^2
cosa2a =（1-tana^2)/(1+tana^2)=4/5

Answer 4

tan（a+π/4）=（1+tana）/（1-tana）=2 ∴tana=1/3
万能公式cos2a=（1-tan²a）/（1+tan²a）=4/5