a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)

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a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)
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a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)
a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)

a为锐角 cos(a+π/6)=4/5 求sin(2a+π/12)

a是锐角
π/2

sin(2a+π/12)=cos[2(a+π/6)-π/4]=√2/2(cos[2(a+π/6)]+sin[2(a+π/6)])
因为cos(a+π/6)=4/5,所以sin(a+π/6)=3/5
cos[2(a+π/6)]=2[cos(a+π/6)]²-1=7/25,sin[2(a+π/6)]=cos(a+π/6)*sin(a+π/6)=24/25。
所以结果为√2/2*(31/25)=31√2/50.