Question

已知角a为锐角,sin(A+15°)=4/5,则cos(2A-15°)=

Answer 1

角A为锐角,sin(A+15°)=4/5,

∴cosA=cos[(A+15°)-15°]=cos(A+15°)cos15°+sin(A+15°)sin15°>0,

∴cos(A+15°)=3/5,

∴sin2(A+15°)=24/25,

cos2(A+15°)=1-2[sin(A+15°)]^2=1-32/25=-7/25,

∴cos(2A-15°）=cos[2(A+15°)-45°]=(-7+24)/(25√2)=17√2/50>0,

-15°