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、设a为锐角,若cos(a+pi/6)=4/5,则sin(2a+pi/12)的值为?(问题同上)求高手相助.深夜打扰真过意不去,还望海涵.

题目详情
、设a为锐角,若cos(a+pi/6)=4/5,则sin(2a+pi/12)的值为?
(问题同上)
求高手相助.深夜打扰真过意不去,还望海涵.
▼优质解答
答案和解析
a为锐角,cos(a+π/6)=4/5
所以,sin(a+π/6)=3/5
sin(2a+π/3)=2sin(a+π/6)cos(a+π/6)=2×(3/5)×(4/5)=24/25
cos(2a+π/3)=cos²(a+π/6)-sin²(a+π/6)=16/25-9/25=7/25
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)×(√2/2)-(7/25)×(√2/2)
=17√2/50