求sin(a+75)+cos(a+45)—根号3cos(a+15)等于几

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求sin(a+75)+cos(a+45)—根号3cos(a+15)等于几

求sin(a+75)+cos(a+45)—根号3cos(a+15)等于几
求sin(a+75)+cos(a+45)—根号3cos(a+15)等于几

求sin(a+75)+cos(a+45)—根号3cos(a+15)等于几
是度吗?
sin(a+75°)+cos(a+45°)—√3cos(a+15°)
=sin(a+75°)+sin(90°-a-45°)-√3cos(a+15°)
=sin(a+75°)+sin(45°-a)-√3cos(a+15°)
=2sin60°cos(a+15°)-√3cos(a+15°)
=√3cos(a+15°)-√3cos(a+15°)
=0.

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
=(√3/2-√3/2)sint+(1/2+1-3/2)cost
=0+0=0