Question

cos15度减sin15度的值是多少?(过程)

Answer 1

cos30°=1-2sin²15°

sin15°=√[(1-√3/2)/2]=√[(2-√3)/4]=√[(4-2√3)]/√8=(√3-1)/2√2=(√6-√2)/4

cos30°=2cos²15°-1

cos15°=√[(1+√3/2)/2]=√[(2+√3)/4]=......=(√6+√2)/4

∴cos15°-sin15°=(√6+√2)/4-(√6-√2)/4=(√6+√2-√6+√2)/4

=2√2/4=√2/2

Answer 2

cos15=cos(60-45)=cos60cos45+sin60sin45=1/2*根号2/2+根号3/2*根号2/2=(根号2+根号6）/4
sin15=sin（60-45）=sin60cos45-cos60sin45=根号3/2*根号2/2-1/2*根号2/2=根号6-根号2）/4