Question

设α为锐角，若cos(α+π/6)=3/5，则sin(α-π/12)=

设α为锐角，若cos(α+π/6)=3/5，则sin(α-π/12)=

Answer 1

cos(a+π/6)=3/5
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

Answer 2

罪（2A +π/12）= SIN（2A +π/ 3，π/ 4）
订购+π/ 6 = X

所以简化成罪（2X-π/ 4）=sin2xcosπ / 4-cos2xsinπ/ 4 =2sinxcosxcosπ/4-（2cosxcosx-1）sinπ/ 4

入已知条件cosx = 0/5的sinx = 4/5
获得未知的公式= 2 * 0.8 * 0.6 *cosπ/4-7/25sinπ/4= 17/25 *（1/2）^ 1/2