已知tana+cota=5/2,求cos2a和sin(2a+π/4)
问题描述:
已知tana+cota=5/2,求cos2a和sin(2a+π/4)
如题
答
tana+cota=sina/cosa+cosa/sina=[(sina)^2+(cosa)^2]/sinacosa=1/(1/2sin2a)=5/2
sin2a=4/5
cos2a=3/5或-3/5
sin(2a+π/4)=sin2acosπ/4+sinπ/4cos2a=7√2/10或√2/10