equation with trig?

Question

can someone show me the steps of making this equation as simple as possible to graph them!!!

1) y=1-cos(2x-pi/3)

2) y= -cot(3x - pi/4)


3) y= - 3sec(2pix - pi/4)

Answer 1

1) y=1-cos(2x-pi/3)
we know
1-cosA=2sin^2(A/2)
so y=2sin^2((2x-pi/3)/2)
y=2sin^2(x-pi/6)
2) y= -cot(3x - pi/4)
y=cot(pi/4-3x)
3) y= - 3sec(2pix - pi/4)
y= 3cosec(pi+2pix - pi/4)
y= 3cosec(2pix +3 pi/4)
y= 3cosec[pi(2x +3/4)]

Answer 2

they're already easy to graph, note that for the first
1 - cos (2x - pi/3) = 1 - cos (pi/3 - 2x)