Question

高一数学 求解题过程

cos7°-cos8°cos15°/cos23°-cos8°cos15° 化简=

cosx+cos(x+60°） 化简

Answer 1

(cos7-cos8*cos15)/(cos23-cos8*cos15)
=[cos(15-8)-cos8*cos15]/[cos(15+8)-cos8*cos15]
=(cos15cos8+sin15sin8-cos8cos15)/(cos15cos8-sin15sin8-cos8cos15)
=sin15sin8/(-sin15sin8)
=-1

cosx+cos(x+60)
=cosx+cosxcos60-sinxsin60
=cosx+1/2cosx-根号3/2sinx
=3/2cosx-根号3/2sinx
=根号3（根号3/2cosx-1/2sinx)
=根号3(cos30cosx-sin30sinx)
=根号3cos( x+30)