化简：cos^(@+15度)+sin^(@-15度)+sin(@+180度)cos(@-180度)_数学解答

化简：cos^(@+15度)+sin^(@-15度)+sin(@+180度)cos(@-180度)

人气：192 ℃　时间：2020-04-12 18:42:09

解答

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+1/2(-2sin2asin30)-1/2sin2a
=1-1/2sin2a-1/2sin2a
=1