化简cos(派/2 a)-tan(派/2－a)*sin(派/2 a)的结果是?

题目

化简cos(派/2 a)-tan(派/2－a)*sin(派/2 a)的结果是?

答案

simple(X)
simplify:
-sin((- 2*a^2 + pi)/(2*a))/sin(a)
radsimp:
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
simplify(100):
sin(a - pi/(2*a))/sin(a)
combine(sincos):
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
combine(sinhcosh):
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
combine(ln):
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
factor:
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
expand:
cos(pi/(2*a)) - sin(pi/(2*a))/tan(a)
combine:
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
rewrite(exp):
exp(-(pi*i)/(2*a))/2 + exp((pi*i)/(2*a))/2 - (((exp(-(pi*i)/(2*a))*i)/2 - (exp((pi*i)/(2*a))*i)/2)*(exp(- pi*i + a*2*i)*i - i))/(exp(- pi*i + a*2*i) + 1)
rewrite(sincos):
cos(pi/(2*a)) + (sin(a - pi/2)*sin(pi/(2*a)))/cos(a - pi/2)
rewrite(sinhcosh):
cosh((pi*i)/(2*a)) + (sinh((pi*i)/2 - a*i)*sinh((pi*i)/(2*a)))/cosh((pi*i)/2 - a*i)
rewrite(tan):
(2*tan(a - pi/2)*tan(pi/(4*a)))/(tan(pi/(4*a))^2 + 1) - (tan(pi/(4*a))^2 - 1)/(tan(pi/(4*a))^2 + 1)
mwcos2sin:
1 - (sin(a - pi/2)*sin(pi/(2*a)))/(2*sin(a/2 - pi/4)^2 - 1) - 2*sin(pi/(4*a))^2
collect(a):
cos(pi/(2*a)) + sin(pi/(2*a))*tan(a - pi/2)
ans =
sin(a - pi/(2*a))/sin(a)