求下列各式的值sin15cos15;cos²π/8-sin²π/8tan22.5/1-tan²22.5；2cos²22.5-1

Question

求下列各式的值
sin15cos15;
cos²π/8-sin²π/8
tan22.5/1-tan²22.5；
2cos²22.5-1

Answer 1

1,sin60=sin(45+15)=sin45cos15+sin15cos45
sin30=sin(45-15)=sin45cos15-sin15cos45 相加 sin45cos15=（√3+1）/4
2,cos2a=cos²a-sin²a cos²π/8-sin²π/8=cosπ/4=√2/2
3,tan45=tan2×22.5 =2tan22.5/1-tan²22.5 tan22.5/1-tan²22.5=（tan45）/2=1/2
4,2cos²22.5-1=cos2×22.5=cos45=√2/2