角A为锐角,A+六分之π的余弦值为5分之4,求2A - 知识问答

角A为锐角,A+六分之π的余弦值为5分之4,求2A+十二分之π的正弦值.各位大神帮帮小弟啊!

1个回答

角A为锐角,cos(A+π/6)=4/5
∴sin(A+π/6)=3/5
∴cos(2A+π/3)=2*cos²(A+π/6)-1=7/25
sin(2A+π/3)=2sin(A+π/6)cos(A+π/6)=24/25
sin(2A+π/12)=sin(2A+π/3-π/4)
=sin(2A+π/3)*cos(π/4)-cos(2A+π/3)*sin(π/4)
=(24/25-7/25)*√2/2=7√2/25

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