tan(−150°)•cos(−570°)•cos(−1140°)tan(−210°)•sin(−690°)=3232．

Question

(tan(−150°)•cos(−570°)•cos(−1140°))/(tan(−210°)•sin(−690°))=

(√(3))/(2)

(√(3))/(2)

．(tan(−150°)•cos(−570°)•cos(−1140°))/(tan(−210°)•sin(−690°))=

(√(3))/(2)

(√(3))/(2)

．(tan(−150°)•cos(−570°)•cos(−1140°))/(tan(−210°)•sin(−690°))tan(−150°)•cos(−570°)•cos(−1140°)tan(−150°)•cos(−570°)•cos(−1140°)tan(−210°)•sin(−690°)tan(−210°)•sin(−690°)

(√(3))/(2)

(√(3))/(2)(√(3))/(2)√(3)√(3)√(3)

3

322

(√(3))/(2)

(√(3))/(2)(√(3))/(2)√(3)√(3)√(3)

3

322

Answer 1

原式=(−tan150°cos570°cos1140°)/(tan210°sin690°)=-(tan(180°−30°)cos(720°−150°)cos(3×360°+60°))/(tan(180°+30°)sin(720°−30°))=-(−(√(3))/(3)×(−(√(3))/(2))×(1)/(2))/((√(3))/(3)×(−(1)/(2)))=(√(3))/(2)．
故答案为：(√(3))/(2) (−tan150°cos570°cos1140°)/(tan210°sin690°)−tan150°cos570°cos1140°−tan150°cos570°cos1140°−tan150°cos570°cos1140°tan210°sin690°tan210°sin690°tan210°sin690°=-(tan(180°−30°)cos(720°−150°)cos(3×360°+60°))/(tan(180°+30°)sin(720°−30°))=-(−(√(3))/(3)×(−(√(3))/(2))×(1)/(2))/((√(3))/(3)×(−(1)/(2)))=(√(3))/(2)．
故答案为：(√(3))/(2) (tan(180°−30°)cos(720°−150°)cos(3×360°+60°))/(tan(180°+30°)sin(720°−30°))tan(180°−30°)cos(720°−150°)cos(3×360°+60°)tan(180°−30°)cos(720°−150°)cos(3×360°+60°)tan(180°−30°)cos(720°−150°)cos(3×360°+60°)tan(180°+30°)sin(720°−30°)tan(180°+30°)sin(720°−30°)tan(180°+30°)sin(720°−30°)=-(−(√(3))/(3)×(−(√(3))/(2))×(1)/(2))/((√(3))/(3)×(−(1)/(2)))=(√(3))/(2)．
故答案为：(√(3))/(2) (−(√(3))/(3)×(−(√(3))/(2))×(1)/(2))/((√(3))/(3)×(−(1)/(2)))−(√(3))/(3)×(−(√(3))/(2))×(1)/(2)−(√(3))/(3)×(−(√(3))/(2))×(1)/(2)−(√(3))/(3)√(3)√(3)√(3)

3

33333×(−(√(3))/(2)√(3)√(3)√(3)

3

33222)×(1)/(2)111222(√(3))/(3)×(−(1)/(2))(√(3))/(3)×(−(1)/(2))(√(3))/(3)√(3)√(3)√(3)

3

33333×(−(1)/(2)111222)=(√(3))/(2)．
故答案为：(√(3))/(2) (√(3))/(2)√(3)√(3)√(3)

3

33222．
故答案为：(√(3))/(2) (√(3))/(2)√(3)√(3)√(3)

3

33222