Question

cos(a＋15)＋sin（a－15）＋sin（a＋180）cos（a－180）化简

cos(a＋15)＋sin（a－15）＋sin（a＋180）cos（a－180）化简

Answer 1

cos²(a+15)+sin²(a-15)+sin(a+180)cos(a-180) =cos²(a+15)+sin²(a+15)-sin²(a+15)+sin²(a-15)+sinacosa =1+[sin²(a-15)-sin²(a+15)]+sinacosa =1+[sin(a-15)+sin(a+15)][sin(a-15)-sin(a+15)]+sinacosa =1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa =1-sin2a*sin30+(1/2)*sin2a =1-(1/2)*sin2a+(1/2)*sin2a =1

Answer 2

cos^2(a+15)+sin^2(a-15)+sin(a+180)cos(a-180)
=cos^2(a+15)+sin^2(a-15)+sinacosa
=[cos2(a+15)+1]/2+[1-cos2(a-15)]/2+sinacosa
=1+1/2[cos(2a+30)-cos(2a-30)]+1/2sin2a
=1+1/2(cos2acos30-sin2asin30-cos2acos30-sin2asin30)-1/2sin2a
=1-sin2a*sin30+(1/2)*sin2a
=1-(1/2)*sin2a+(1/2)*sin2a
=1