For part a), use these double angle formulae:
#sin2x=2sinxcosx#
#cos2x=2cos^2x-1#
Now here's the problem:
#color(white)=(sin2t)/(1+cos2t)#
#=(2sintcost)/(1+cos2t)#
#=(2sintcost)/(1+2cos^2t-1)#
#=(2sintcost)/(color(red)cancelcolor(black)(1-1)+2cos^2t)#
#=(2sintcolor(red)cancelcolor(black)(cost))/(2cos^color(red)cancelcolor(black)2t)#
#=(color(red)cancelcolor(black)2sint)/(color(red)cancelcolor(black)2cost)#
#=sint/cost#
#=tant#
Here's the graph:
graph{(sin(2x))/(1+cos(2x)) [-10, 10, -5, 5]}
For part b), use these cofunction identities:
#sin(x-pi/2)=cosx#
#sec(x+pi/2)=-cscx#
Now here's the problem:
#color(white)=(sin(pi/2-x)sec(x+pi/2))/cscx#
#=(cosxsec(x+pi/2))/cscx#
#=(cosx(-cscx))/cscx#
#=(cosx*-color(red)cancelcolor(black)cscx)/color(red)cancelcolor(black)cscx#
#=cosx*-1#
#=-cosx#
Here's the graph:
graph{(sin(pi/2-x)*sec(x+pi/2))/(csc(x)) [-10, 10, -5, 5]}
