设a为锐角,若cos(a+π⼀6)=4⼀5,则sin(2a+π⼀12)的值为多少

2025-03-24 07:16:42
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回答1:

a是锐角
π/2cos(a+π/6)=4/5,sin(a+π/6)=3/5
sin(2a+π/3)
=2sin(a+π/6)cos(a+π/6)
=2*(4/5)*(3/5)
=24/25cos(2a+π/3)
=2cos�0�5(a+π/6)-1
=2*(4/5)�0�5-1
=7/25sin(2a+π/12)
=sin[(2a+π/3)-π/4]
=sin(2a+π/3)cos(π/4)-cos(2a+π/3)cos(π/4)
=(24/25)*(√2/2)-(7/25)*(√2/2)
=17√2/50