wep.
trig1.
y
cos(A)+cos(B)=>2*cos((A+B)/2)*cos((A-B)/2).


cossum.
n.
add new rule.
auto1.
n
sin(x)+sin(3*x) + 2*sin(2*x) = 0.
2*sin(2*x)*cos(x) + 2*sin(2*x) = 0.
sin(A)+sin(B)=>2*sin((A+B)/2)*cos((A-B)/2).


sinsum.
add new rule.
auto1.
n
sin(3*x)-sin(x) + 2*cos(2*x) = 0.
2*sin(x)*cos(2*x) + 2*cos(2*x) = 0.
sin(A)-sin(B)=>2*cos((A+B)/2)*sin((A-B)/2).


sindiff.
add new rule.
auto1.
n
cos(x)-cos(3*x) + 2*sin(2*x) = 0.
2*sin(2*x)*sin(x) + 2*sin(2*x) = 0.
cos(A)-cos(B)=>2*sin((A+B)/2)*sin((B-A)/2).


cosdiff
writeall(dump2).
[we].
example1.
y
A*cos(X)+B*sin(X)=>(A^2 + B^2)^(1/2)*sin(X+arctan(B/A)).


n
add new rule.
'Collection'.
cos(x)+ 2*sin(x) = 1.
5^(1/2)*sin(x+arctan(2)) = 1.
cos(X)+B*sin(X)=>(1 + B^2)^(1/2)*sin(X+arctan(B)).


add new rule.
'Collection'.
2*cos(x) + sin(x) = 1.
5^(1/2)*sin(x+arctan(1/2)) = 1.
A*cos(X)+ sin(X)=>(A^2 + 1)^(1/2)*sin(X+arctan(1/A)).


add new rule.
'Collection'.
cos(x) + sin(x) = 1.
2^(1/2)*sin(x+arctan(1)) = 1.
cos(X)+sin(X) => 2^(1/2)*sin(X+arctan(1)).


writeall(dump3).
trig3.
y
sin(A)+cos(A)=0=>tan(A) = -1.


tanrule.
n
add new rule.
auto5.
y
sinsum.
add new rule.
auto5.
y
sindiff.
add new rule.
auto5.
y
cosdiff.
writeall(dump4).
trig2.
y
sin(A)=>2*sin(A/2)*cos(A/2).


sinhalf.
n
add new rule.
auto7.
y.
cosdiff.
add new rule.
auto7.
y.
sindiff.
add new rule.
auto7.
y.
sinsum.
writeall(dump5).
usefulprob.
trig4.
writeall(dump6).
halt.

















