已知0<x<派/2,sinx=4/5(1)求tanx的值,(2)求cos2x+sin(x+派/2)的值

问题描述:

已知0<x<派/2,sinx=4/5(1)求tanx的值,(2)求cos2x+sin(x+派/2)的值

1)∵0<x<派/2,sinx=4/5 ∴cosx=√(1-16/25)=3/5 ∴tanx=sinx/cosx=(4/5)/(3/5)=4/3 2)cos2x+sin(x+π/2) =2cosx-1+sin(π-π/2-x) =2cosx-1+sin(π/2-x) =2cosx-1+cosx =2(3/5)-1+3/5 =18/25-1+15/25 =8/25