已知sin(a/2+π/6)=1/4求sin(π/6+a)

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已知sin(a/2+π/6)=1/4求sin(π/6+a)

已知sin(a/2+π/6)=1/4求sin(π/6+a)
已知sin(a/2+π/6)=1/4求sin(π/6+a)

已知sin(a/2+π/6)=1/4求sin(π/6+a)
∵sin(½a+π/6)=¼,
∴(½a+π/6)∈(2kπ,2kπ+π/6)U(2kπ+5π/6,2kπ+π),
(a+π/3)∈(4kπ,4kπ+π/3)U(4kπ+5π/3π,4kπ+2π)
∴cos(a+π/3)=1-2sin²(½a+π/6)=7/8,
sin(a+π/3)=±√1-cos²(a+π/3)=±√15/8.
∴sin(a+π/6)=sin[(a+π/3)-π/6]
=sin(a+π/3)cos(π/6)-cos(a+π/3)sin(π/6)
=(±√15/8)·(√3/2)-(7/8)·(1/2)
=(±3√5-7)/16.