Question

求下列各式的值 已知cos(a-π/3)=12/13，π/3小于a小于π/2，求cosa

急 在线等

Answer 1

因为cos(a-π/3)=12/13，π/3<a<π/2
所以sin(a-π/3)=√[1-(12/13)²]=5/13
cosa=cos[(a-π/3)+π/3]=cos(a-π/3)cosπ/3-sin(a-π/3)sinπ/3
=(12/13)*(1/2)-(5/13)*(√3/2)=(12-5√3)/26

Answer 2

π/3<a<π/2
π/2-π/3>a-π/3>0
sin (a-π/3)=5/13
cosa=cos(a-π/3+π/3)=cos(a-π/3)cosπ/3-sin(a-π/3)sin(π/3)
=(12/13)(1/2)-(5/13)(√3/2)
=(12-5√3)/26