sin(a+75度)+cos(a+45度)-根号3cos(a+15)度的值
sin(a+75度)+cos(a+45度)-根号3cos(a+15)度的值
原式=sin(a+75°)+sin(45°-a)-√3sin(a+15°)
=2sin60°cos(15°+a)-√3sin(a+15°)
=√3cos(15°+a)-√3sin(a+15°)
=√3[sin(75°-a)-sin(a+15°)]
=2√3cos45°sin(30°-a)
=√6sin(30°-a)
原式=sin [ ( A+ 45 ) + 30 ] + cos ( A + 45 ) - 3^ ( 1 / 2 ) cos ( A + 15 )=sin ( A + 45 ) cos 30 + sin 30 cos ( A + 45) -3 ^ ( 1 / 2 ) cos ( A + 15 ) = sin ( A + 15 ) - 3 ^ ( 1 / 2 ) cos ( A + 15 ) = 2sin (A + 75 )
手都打疼了
设a+45=t∴sin(a+75)+cos(a+45)-√3cos(a+15)=sin(t+30)+cost-√3cos(t-30)=sintcos30+sin30cost+cost-√3(costcos30+sintsin30)=(√3/2)sint+(1/2)cost+cost-(3/2)cost-(√3/2)sint=0
sin(a+75°)+cos(a+45°)-√3cos(a+15°)
=cos(a-15°)+cos(a+45°)-√3cos(a+15°)
=2cos[(a-15°+a+45°)/2]cos[a+45°-a+15°)/2]-√3cos(a+15°)
=2cos(a+15°)cos30°-√3cos(a+15°)
=0