Question

一道高一的数学题目

求tan9+cot117-tan43-cot351的值
希望能有详细的解答过程!
拜托了!

Answer 1

tan9+cot117-tan243-cot351
=tan9+cot9-tan63-cot63
=sin9/cos9+cos9/sin9-sin63/cos63-cos63/sin63
=[(sin9)^2+(cos9)^2]/(sin9cos9)-[(sin63)^2+(cos63)^2]/(sin63cos63)
=2/sin18-2/sin126
=2/sin18-2/sin54
=2(sin54-sin18)/(sin18sin54)
=4(sin18cos36)/(sin18sin54)
=4(sin18sin54)/(sin18sin54)
=4.

Answer 2

tan(9)+cot(117)-tan(43)-cot(351) = 2.9596912939842
计算器算的