化简下列各式．（1）1+2sin280°cos440°sin260°+cos800°；（2）sin(2π−α)cos(α−7π2)sin(3π2+α)cos(2π+α)+tan(3π−α)sin(π−α)cos(π+α)．

Question

化简下列各式．
（1）(√(1+2sin280°cos440°))/(sin260°+cos800°)；
（2）(sin(2π−α)cos(α−(7π)/(2)))/(sin((3π)/(2)+α)cos(2π+α))+(tan(3π−α))/(sin(π−α)cos(π+α))．

Answer 1

（1）原式=(√(1−2sin80°cos80°))/(−sin80°+cos80°)=(|sin80°−cos80°|)/(−sin80°+cos80°)=(sin80°−cos80°)/(−(sin80°−cos80°))=-1；
（2）原式=(−sinα(−sinα))/(−cosαcosα)+(−tanα)/(sinα(−cosα))=-tan²α+(1)/(cos2α)=-tan²α+tan²α+1=1．