sin157°30′cos22°30′
=sin(180-22°30′)cos22°30′
=sin22°30′cos22°30′
=1/2*sin(2*22°30′)
=1/2*sin(45°)
=√2
sin(2π-α)=-sinα=-4/5
sinα=4/5
π/2<α<π
所以cosα<0
sin²α+cos²α=1
所以cosα=-3/5
所以tan(π+α)
=tanα
=sinα/cosα
=-4/3