#secA+cscA=2#
#1/cosA+1/sinA=2#
#(sinA+cosA)/(sinA*cosA)=2#
#sinA+cosA=2sinA*cosA#
#sinA+cosA=sin2A#
#sinA+cosA=(sinA+cosA)^2-1#
After setting #B=sinA+cosA#, this equation became
#B=B^2-1#
#B^2-B-1=0#
From it, #B_1=(1+sqrt5)/2# and #B_2=(1-sqrt5)/2#
#a)# For #B_1=(1+sqrt5)/2#,
#sinA+cosA=(1+sqrt5)/2#
#sinA=(1+sqrt5)/2-cosA#
#(sinA)^2=((1+sqrt5)/2-cosA)^2#
#1-(cosA)^2=(3+sqrt5)/2-(sqrt5+1)*cosA+(cosA)^2#
#2(cosA)^2-(sqrt5+1)*cosA+(sqrt5+1)/2=0#
#Delta=(sqrt5+1)^2-4*2*(sqrt5+1)/2=-3*(sqrt5+1)^2<0#
Hence, no solution for #B=(sqrt5+1)/2#
#b)# For #B_1=(1-sqrt5)/2#,
#sinA+cosA=(1-sqrt5)/2#
#sinA=(1-sqrt5)/2-cosA#
#(sinA)^2=((1-sqrt5)/2-cosA)^2#
#1-(cosA)^2=(3-sqrt5)/2+(sqrt5-1)*cosA+(cosA)^2#
#2(cosA)^2+(sqrt5-1)*cosA-(sqrt5-1)/2=0#
Set #y=cosA#, this equation became,
#2y^2+(sqrt5-1)*y-(sqrt5-1)/2=0#
#Delta=(sqrt5-1)^2-4*2*(-(sqrt5+1)/2)=5*(sqrt5-1)^2=(5-sqrt5)^2>0#
#y_1=[-(sqrt5-1)+(5-sqrt5)]/4=(3-sqrt5)/2#
#y_2=[-(sqrt5-1)-(5-sqrt5)]/4=-1#
However, #y_2=-1# doesn't provide original equation. Hence,
#cosA=(3-sqrt5)/2#
