Question

已知sin(π-α)-cos(π+α)=根2/3其中,0<α<π,求tanα

已知sin(π-α)-cos(π+α)=根2/3其中,0<α<π,求tanα

Answer 1

已知sin(π-α)-cos(π+α)=根2/3其中,0<α<π,求tanα

sin(π-α)-cos(π+α)=√2/3
sinα-cosα=√2/3
(sinα-cosα)^2=2/9
1-2sinαcosα=2/9
2sinαcosα=7/9 (0<α<π)
所以cosα>0
sin2α=7/9
cos2α=√[1-(7/9)^2]
=√[1-49/81]
=4√2/9

tanα=(1-cos2α)/sin2α
=(1-4√2/9)/(7/9)
=(9-4√2)/9*9/7
=(9-4√2)/7