1) simplifying 1/sin(pi/18)-(sqrt(3))/cos(pi/18),  time: 0.015487 sec
Result: 0
Ordinary simplification: 0

2) simplifying cos(2*x)/(sin(x)+cos(x))^2+2*(sin(x)^3-cos(x)^3)/(sin(x)+cos(x)),  time: 0.006205 sec
Result: -cos(2*x)
Ordinary simplification: -cos(2*x)

3) simplifying sin(3*pi/4-2*x)^2-sin(7*pi/6-2*x)^2-sin(13*pi/12)*cos(11*pi/12-4*x),  time: 0.266751 sec
Result: sin(4*x)
Ordinary simplification: (sqrt(2)+sqrt(6))/16*sqrt(2)*cos(4*x)+(sqrt(2)-sqrt(6))/16*sqrt(2)*sin(4*x)+(-sqrt(2)-sqrt(6))/16*sqrt(6)*cos(4*x)+(-sqrt(2)+sqrt(6))/16*sqrt(6)*sin(4*x)+1/4*cos(4*x)+(sqrt(3)+2)/4*sin(4*x)

4) simplifying sin(x)^6+cos(x)^6-4/4*(sin(x)^2-cos(x)^2)^2,  time: 0.008253 sec
Result: 1/8-1/8*cos(4*x)
Ordinary simplification: -1/8*cos(4*x)+1/8

5) simplifying sin(3*x)/sin(x)-cos(3*x)/cos(x),  time: 0.001293 sec
Result: 2
Ordinary simplification: 2

6) simplifying cos(pi/9)*cos(2*pi/9)*cos(3*pi/9)*cos(4*pi/9),  time: 0.001323 sec
Result: 1/16
Ordinary simplification: 1/16

7) simplifying 3*sin(x)-4*sin(x)^3,  time: 0.007647 sec
Result: sin(3*x)
Ordinary simplification: -4*sin(x)^3+3*sin(x)

8) simplifying (10*cos(x)+5*cos(3*x)+cos(5*x))/16,  time: 0.013443 sec
Result: cos(x)^5
Ordinary simplification: 5/16*cos(3*x)+1/16*cos(5*x)+5/8*cos(x)

9) simplifying (3-4*cos(2*x)+cos(4*x))/(3+4*cos(2*x)+cos(4*x)),  time: 0.041658 sec
Result: tan(x)^4
Ordinary simplification: (cos(2*x)^2-2*cos(2*x)+1)/(cos(2*x)^2+2*cos(2*x)+1)

10) simplifying 2*pi*sin(a*pi)/(1-cos(2*a*pi)),  time: 0.935537 sec
Result: 0
Ordinary simplification: (pi*cos(2*a*pi)*sin(a*pi)-pi*cos(a*pi)*sin(2*a*pi)-pi*sin(a*pi))/(cos(2*a*pi)-1)+i*(-pi*cos(2*a*pi)*cos(a*pi)+pi*cos(a*pi)-pi*sin(2*a*pi)*sin(a*pi))/(cos(2*a*pi)-1)

11) simplifying sin(2*x)^3*cos(6*x)+cos(2*x)^3*sin(6*x),  time: 0.020862 sec
Result: 3/4*sin(8*x)
Ordinary simplification: 3/4*sin(8*x)

12) simplifying (sin(x-a)/sin(x-b)*cos(x-a)/cos(x-b)+1)/(cos(x-a)/cos(x-b)+sin(x-a)/sin(x-b)),  time: 0.007664 sec
Result: cos(a-b)
Ordinary simplification: cos(a-b)

13) simplifying 1/tan(7*pi/18)+4*cos(7*pi/18),  time: 0.037397 sec
Result: sqrt(3)
Ordinary simplification: sqrt(3)

14) simplifying sin(6*x)-2*sqrt(3)*cos(3*x)^2+sqrt(3),  time: 0.048838 sec
Result: 2*cos(6*x-5/6*pi)
Ordinary simplification: -sqrt(3)*cos(6*x)+sin(6*x)

15) simplifying sum(sin(k*x),k=(1 .. 5))/sum(cos(k*x),k=(1 .. 5)),  time: 0.02071 sec
Result: tan(3*x)
Ordinary simplification: (4*cos(x)^2*sin(x)-sin(x))/(4*cos(x)^3-3*cos(x))

16) simplifying (1+sin(x))/(1-sin(x))+(sin(x)-1)/(sin(x)+1),  time: 0.010056 sec
Result: 4*tan(x)/cos(x)
Ordinary simplification: -4*sin(x)/(sin(x)^2-1)

17) simplifying (sin(x+y)-sin(x-y))/(cos(x+y)+cos(x-y)),  time: 0.033879 sec
Result: tan(y)
Ordinary simplification: (-cos(x+y)*sin(x-y)+cos(x-y)*sin(x+y))/(cos(x+y)*cos(x-y)+sin(x+y)*sin(x-y)+1)

18) simplifying (sin(x)^3-cos(x)^3)/(sin(x)-cos(x)),  time: 0.009943 sec
Result: 1/2*sin(2*x)+1
Ordinary simplification: 1/2*sin(2*x)+1

19) simplifying tan(x)+cos(x)/(1+sin(x)),  time: 0.005053 sec
Result: 1/cos(x)
Ordinary simplification: 1/cos(x)

20) simplifying 1/(1+cos(x))+1/(1-cos(x)),  time: 0.006013 sec
Result: 2/sin(x)^2
Ordinary simplification: -2/(cos(x)^2-1)

21) simplifying (sin(3*x)+sin(7*x))/(cos(3*x)-cos(7*x)),  time: 0.02744 sec
Result: 1/tan(2*x)
Ordinary simplification: (-2*cos(x)^2*sin(x)+sin(x))/(2*cos(x)^3-2*cos(x))

22) simplifying (tan(a+b)-tan(b))/(1+tan(a+b)*tan(b)),  time: 0.180323 sec
Result: tan(a)
Ordinary simplification: (-2*cos(a+b)^2*cos(b)*sin(b)+2*cos(a+b)*cos(b)^2*sin(a+b)-cos(a+b)*sin(a+b)+cos(b)*sin(b))/(2*cos(a+b)^2*cos(b)^2-cos(a+b)^2+2*cos(a+b)*cos(b)*sin(a+b)*sin(b)-cos(b)^2+1)

23) simplifying cos(x)^2/(1-sin(x)),  time: 0.004736 sec
Result: sin(x)+1
Ordinary simplification: sin(x)+1

24) simplifying 1-1/4*sin(2*a)^2-sin(b)^2-cos(a)^4,  time: 0.011024 sec
Result: sin(a)^2-sin(b)^2
Ordinary simplification: -1/2*cos(2*a)+1/2*cos(2*b)

25) simplifying sin(10*x)/(sin(x)+sin(9*x)),  time: 0.030512 sec
Result: cos(5*x)/cos(4*x)
Ordinary simplification: (16*cos(x)^5-20*cos(x)^3+5*cos(x))/(8*cos(x)^4-8*cos(x)^2+1)

