∠A是锐角,cos(A+π⼀6)=4⼀5,则sin(2A+π⼀12)=?

2025-01-31 18:56:24
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回答1:

∠A是锐角,根据cos(A+π/6)=4/5,∠A+π/6<π/2,∠A<π/3,
所以sin(A+π/6)=3/5,
sin(2A+π/3)=2sin(A+π/6)cos(A+π/6)=24/25,
2A+π/3<π,cos(2A+π/3)=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