Question

设a为锐角，且tana=tan(a+10度)tan(a+20度)tan(a+30度),求a的所有可能值

要有过程啊啊啊啊

Answer 1

用Forcal求解：
!using["fcopt","math"];
f(a)=tan(a)-tan(a+10/180*pi)*tan(a+20/180*pi)*tan(a+30/180*pi);
isolve[HFor("f")];

有无数解（弧度表示），列举一部分：
8.726646259971635e-002 0.
0.174532925199433 0.
3.22885911618951 5.551115123125783e-017
3.316125578789227 -1.665334536937735e-016
4.799655442985034 1.994848730646481e-011
6.370451769777143 -5.250383461330443e-013
6.45771823237902 2.775557561562891e-017
8.028514572960381 -1.254190982180603e-007
9.512044423368547 -1.332545185306344e-013
9.599310885968814 1.665334536937735e-016
11.17010721276374 -2.202682480856311e-013
12.65363707695926 9.081624341433781e-014
12.74090353955861 2.220446049250313e-016
14.3116998663535 7.105427357601002e-015
15.79522973054814 -1.324357290499734e-013
15.88249619314839 -8.326672684688674e-017
17.36602605734223 -4.297540101561026e-011
18.93682238413631 -5.253991686160475e-013
19.0240888467382 -2.498001805406602e-016
20.59488517353309 7.993605777301127e-015
22.07841503772864 9.114931032172535e-014
22.16568150032799 -2.220446049250313e-016
23.73647782712526 -2.157918288503424e-011
25.22000769131844 9.112155474610972e-014
25.30727415391778 -1.942890293094024e-016
26.87807048071268 1.243449787580175e-014
28.36160034490785 -4.440892098500626e-016
28.44886680750757 -1.387778780781446e-016
29.93239667170275 -5.329070518200751e-015
31.50319299849765 4.024558464266193e-016
31.59045946109736 9.436895709313831e-016
33.07398932529255 -3.019806626980426e-014
34.64478565208529 -5.248856904671584e-013
34.73205211468715 -2.498001805406602e-016
36.30284844148205 -2.398081733190338e-014
37.78637830567508 -5.257738688868585e-013
37.87364476827694 7.494005416219807e-016
39.35717463247214 -3.730349362740526e-014
... ...

Answer 2

a约为5°和10°
可用计算器验证。
过程就是用编程方法求解的。
其实5°和10° 非精确值，只是十分接近答案的近似值。

Answer 3

5°、10°