MT【188】一个正切余切有关的恒等式

(2017北大特优)求$9 an 10^circ+2 an 20^circ+4 an 40^circ- an 80^circ=$_____
A．$0$
B.$dfrac{sqrt 3}3$
C．$1$
D．$sqrt 3$

提示:$cot x- an x=2cot(2x)$得答案0