2020-수학-가형-홀수-10¶
문제¶
풀이¶
from sympy import *
a, b, x = symbols("a b x")
b_in_terms_of_a = solve(a+2*b-pi, b)[0]
b_in_terms_of_a
\[\displaystyle - \frac{a}{2} + \frac{\pi}{2}\]
eqn = tan(a+b)+Rational(3,2)
eqn = eqn.subs(b,b_in_terms_of_a)
eqn
\[\displaystyle \frac{3}{2} - \cot{\left(\frac{a}{2} \right)}\]
tan_alpha = expand_trig(tan(2*x)).subs(x,a/2)
tan_alpha
\[\displaystyle \frac{2 \tan{\left(\frac{a}{2} \right)}}{1 - \tan^{2}{\left(\frac{a}{2} \right)}}\]
t = Symbol('t')
tan_alpha.subs(tan(a/2),Rational(2,3))
\[\displaystyle \frac{12}{5}\]
alpha = solveset(eqn, a, Interval(0,pi))
alpha = list(alpha)[0]
print(alpha.evalf())
tan(alpha)
1.17600520709514
\[\displaystyle \frac{12}{5}\]