若tanα+1/tanα=10/3,α∈[(4/π),(2/π)],则[2α+(π/4)]的值为————

Question

若tanα+1/tanα=10/3,α∈[(4/π),(2/π)],则[2α+(π/4)]的值为————

Answer 1

3(tanα)^2-10tanα+1=0,
(3tanα-1)(tanα-3)=0,
tanα=1/3,或tanα=3,
∵α∈(π/4,π/2),
∴tanα=3,
tan2α=2tanα/[1-(tanα)^2]
=2*3/(1-9)=-3/4,
tan(2α+π/4)=(tan2α+tanπ/4)/[1-tan2αtanπ/4]
=(-3/4+1)/(1+3/4)
=(1/4)/(7/4)
=1/7,
是求tan(2α+π/4)吗?
结果是1/7,
否则,
∵tan(2α+π/4)>0,
2α+π/4应在第三象限,
∴2α+π/4=π+arctan(1/7),