積化和差和差化積記憶口訣及相關(guān)練習(xí)題

sin(A+B)+sin(A—B)=2sinAcosBsin(A+B)—sin(A—B)=2cosAsinBcos(A+B)+cos(A—B)=2cosAcosBcos(A+B)—cos(A—B)=2sinAcosBsin15°sin75°=()

la.?lB.la.?lB.4lC.2D．1sinl05°+sinl5°等于(DVDVsin37.5°cos7.5°=的值為（sin70°cos20°－sinl0°sin50°的值為（A.4A.4lC.2cos72°—cos36°cos72°—cos36°的值為(lB.lB.2lC-_2則厶則厶ABC是（C在△ABC中，若sinAsinB=cos22,A.等邊三角形B.等腰三角形C.角形不等邊三角形D.直角三8.函數(shù)y=sinxcosx的最大值為（）lB.lB.4C.llA.》D壘2

若cos(a+B)cos(a-—B)1則cos2a--sin2B等于9.=3'()2112A.—3B."3C.3D.310．、，（n、函數(shù)y=sinx+可k310．、，（n、函數(shù)y=sinx+可k3丿n—sinx（xU[O,壽]）的值域是（）A．[—2,2]B.12'C.2'D.12'答案1解析：選D.由兩角和與差的正、余弦公式展開左邊可知A、B、C正確.2解析：選B.sin15°sin752解析：選B.sin15°sin75=—2[cos(15°＋75°)—cos(15°—75°)]=—2(cos90°—cos60°)=—2(0—2)=4-3解析：選C.sin105＋sin15°2sin3解析：選C.sin105＋sin15°2sin105°+152105°－15°cos一=2sin60°cos45°2答案:片'=2sin60°cos45°2答案:片'i付1+寸=農(nóng)廣14=2(sin45°+sin30°)4解析：sin37.5°cos7.5°=|[sin(37.5°+7.5°)+sin(37.5°—7.5°)]5解析：選A.sin70°cos20°—sinl0°sin50°=2(sin90°+sin50°)+￡(cos60°－cos40°)=2+扣口50°+4-討40°=|.6解析：選C.原式一2sin72V36°sin72°—36°—2sin54°?sin18°=—2cos36°cos72°=—2?sin|6°=—2?sin|6°cos|6°cos72°sin36°sin72°cos72°sin36°7解析：選B.由已知等式得|[cos(A—B)--cos(A+B)]_2(1+cosC)'sinl44°_1sinl44°_12sin36°°__2'故選C.又A+B_n—C.所以cos(A-B)—cos(n—C)_l+cosC.所以cos(A—B)_1,又一n<A—B<n'所以A—B_0,所以A_B,故AABC為等腰三角形.故選B.8解析：選B.y_sinxsin?xji6卜x?+sinxji68解析：選B.y_sinxsin?xji6卜x?+sinxji6cosx_2_2sin?2x乙l?一_6?2jsin(2x2\6丿??y_maxll4_4.9解析：選C.cos(a+B)cos(a—B)_2(cos2a+cos2B)[(2cos2a—1)+(1—2sin2B)]_cos2a－sin2B'?cos2a－sin2B10解析：選