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Section 5.3
38.
sec(x)+tan(x)=1 .........interval [0,2pi]
1/cos(x)+sin(x)/cos(x)=1
(1+sin(x))/cos(x)=1
1+sin(x)-cos(x)=0
rewrite using identity sin(x)-cos(x)=sqrt(2)sin(x-pi/4)
1+sqrt(2)sin(x-pi/4)=0
sqrt(2)sin(x-pi/4)=-1
sin(x-pi/4)=-1/sqrt(2)
sin(x-pi/4)=-sqrt(2)/2
general solutions:
Radians:
x-pi/4=5pi/4+2pi*k
x-pi/4=7pi/4+2pi*k
solve for x
x=5pi/4+2pi*k+pi/4 =>x=3pi/2+2pi*k
x=7pi/4+2pi*k+pi/4=>x=2pi++2pi*k
solutions for given interval:
x=3pi/2+2pi*k
x=2pi++2pi*k
Degrees:
x=0°
x=360°