Question

已知：cos（15°+α）=3/5 , α为锐角

已知：cos（15°+α）=3/5 , α为锐角
求【tan(435°-α)+sin(α-165°)】/【cos(195°+α)×sin(105°+α)】

Answer 1

α为锐角，cos（15°+α）=3/5>0，则15°+α是锐角，sin(15°+α)=4/5，tan(15°+α)=4/3
[tan(435°-α)+sin(α-165°)]/[cos(195°+α)×sin(105°+α)]
={tan[360°-(15°+α)]+sin[-180°+(15°+α)]}/{cos[180°+(15°+α)]×sin[90°+(15°+α)]}
=[-tan(15°+α)-sin(15°+α)]/[-cos(15°+α)×cos(15°+α)]
=(-4/3-4/5)/[(-3/5)*(3/5)]
=-(32/15)/(-9/25)
=160/27