#1) Pythagorean
f(x)=sin(x)^2+cos(x)^2
show(f(x))
show(f(x).simplify_trig())
show(bool(f(x)==1))
plot(f(x),xmin=-1,xmax=1,ymin=0,ymax=2)
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#2) Pythyagorean
g(x)=f(x)/cos(x)^2
show(g(x))
show(g(x).simplify_trig())
show(bool(g(x)==sec(x)^2))
show(plot(g(x)))
show(plot(sec(x)^2))
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#3) Pythyagorean
h(x)=f(x)/sin(x)^2
show(h(x))
show(h(x).simplify_trig())
show(bool(h(x)==csc(x)^2))
show(plot(h(x),xmin=.1,xmax=2))
show(plot(csc(x)^2,xmin=.1,xmax=2))
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#4) Sum of 2 Angles
var('y')
show(cos(x+y))
show(cos(x+y).simplify_trig())
show(plot3d(cos(x+y),(x,-2,2),(y,-2,2)),viewer='tachyon')
show(plot3d(cos(x)*cos(y)-sin(x)*sin(y),(x,-2,2),(y,-2,2)),viewer='tachyon')
 
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#5) Sum of 2 Angles
var('y')
show(cos(x-y))
show(cos(x-y).simplify_trig())
show(plot3d(cos(x-y),(x,-2,2),(y,-2,2)),viewer='tachyon')
show(plot3d(cos(x)*cos(y)+sin(x)*sin(y),(x,-2,2),(y,-2,2)),viewer='tachyon')
 
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