（1）计算tan(-510°)cos(-210°)cos120°tan(-600°)•sin(-330°)．（2）已知sinα=1213，α∈(π2，π)．求cos(π6-α)的值．

Question

（1）计算(tan(-510°)cos(-210°)cos120°)/(tan(-600°)•sin(-330°))．
（2）已知sinα=(12)/(13)，α∈((π)/(2)，π)．求cos((π)/(6)-α)的值．

Answer 1

（1）原式=(-tan(360°+150°)cos(180°+30°)c0s120°)/(tan(720°-120°)sin(360°-30°))=(tan150°cos30°cos120°)/(tan120°sin30°)=((√(3))/(3)×(√(3))/(2)×(1)/(2))/(-√(3)×(1)/(2))=-(√(3))/(6)；
（2）因为sinα=(12)/(13)，α∈((π)/(2)，π)．所以cosα=-(5)/(13)，所以cos((π)/(6)-α)=cos(π)/(6)cosα+sin(π)/(6)sinα=(√(3))/(2)×(-(5)/(13))+(1)/(2)×(12)/(13)=(12-5√(3))/(26)．