设a为锐角,若cos(a+π/6)=3/5,则sin(a–π/12)的值为?

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设a为锐角,若cos(a+π/6)=3/5,则sin(a–π/12)的值为?
设a为锐角,若cos(a+π/6)=3/5,则sin(a–π/12)的值为?

设a为锐角,若cos(a+π/6)=3/5,则sin(a–π/12)的值为?
a为锐角,cos(a+π/6)=3/5
则:sin(a+π/6)=4/5
sin(a-π/12)=sin[(a+π/6)-π/4]
=sin(a+π/6)cos(π/4)-cos(a+π/6)sin(π/4)
=(4/5)(√2/2)-(3/5)(√2/2)
=√2/10

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