何かいい方法ないですか?

(参考)数学II・数学Ｂ問題
https://www.asahicom.jp/edu/center-exam/shiken2020/pdf2c49z2id/suugaku2_01.pdf
(参考)センター試験解答速報2020＜予備校の東進 ＜「基本的な内容である。」そうです。
https://www.toshin.com/center/sp/

wolframalphaでやってみたい

アイウ=====================
?

エ=======================
?

オカキク================
sin(x)>sqrt(3) cos(x - π/3),0<=x<2*π
https://www.wolframalpha.com/input/?i=sin%28x%29%3Esqrt%283%29+cos%28x+-+%CF%80%2F3%29%2C0%3C%3Dx%3C2*%CF%80&lang=ja
--->(2 π)/3<x<(5 π)/3

ケコサシ===============
25*c*2-35*c+k=0,25*s2-35*s+k=0,c2+s2=1,0<=c<=1,0<=s<=1
https://www.wolframalpha.com/input/?i=25*c2-35*c%2Bk%3D0%2C25*s2-35*s%2Bk%3D0%2Cc2%2Bs*2%3D1%2C0%3C%3Dc%3C%3D1%2C0%3C%3Ds%3C%3D1&lang=ja
--->c = 3/5, k = 12, s = 4/5
--->c = 4/5, k = 12, s = 3/5
--->c = 1/sqrt(2), k = 35/sqrt(2) - 25/2, s = 1/sqrt(2)

25*c*2-35*c+12=0,25*s2-35*s+12=0,c2+s2=1,0<=c<=1,0<=s<=1,s>=c
https://www.wolframalpha.com/input/?i=25*c2-35*c%2B12%3D0%2C25*s2-35*s%2B12%3D0%2Cc2%2Bs*2%3D1%2C0%3C%3Dc%3C%3D1%2C0%3C%3Ds%3C%3D1%2Cs%3E%3Dc&lang=ja
--->c = 3/5, s = 4/5

ソ=====================
25*cos(t)2-35*cos(t)+12=0,25*sin(t)2-35*sin(t)+12=0,0<=t<=pi/2,sin(t)>=cos(t)
wolframalpha.com/input/?i=25*cos%28t%29*2-35*cos%28t%29%2B12%3D0%2C25*sin%28t%29*2-35*sin%28t%29%2B12%3D0%2C0<%3Dt<%3Dpi%2F2%2Csin%28t%29>%3Dcos%28t%29&lang=ja
--->t = 2 tan^(-1)(1/2)

2 tan^(-1)(1/2)*180/pi
https://www.wolframalpha.com/input/?i=2+tan%5E%28-1%29%281%2F2%29*180%2Fpi&lang=ja
--->53.130....

180/4
--->45

180/3
--->60

Sympy onlineでやってみたい

(参考)SymPy Live
https://live.sympy.org/

アイウ==================================
simplify(sqrt(3) *cos(x - pi/3)-sin(x))
print(expand(sqrt(3) *cos(x - pi/3), trig=True))
--->3*sin(x)/2 + sqrt(3)*cos(x)/2

エ======================================
simplify(sqrt(3) *cos(x - pi/3)-sin(x))
print( simplify(sqrt(3) *cos(x - pi/3)-sin(x)) )
--->sin(x + pi/3)

オカキク=================================
solve(sin(x + pi/3)<0)
print(solve(sin(x + pi/3)<0))
--->(2*pi/3 < x) & (x < 5*pi/3)

ケコサシ==================================

ソ========================================

Sympy pythonでやってみたい

作業中