Section 5.3 [ATTACH=full]1363[/ATTACH] [ATTACH=full]1364[/ATTACH]

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°

I didn't know the following trigonometric identity: sin(x)-cos(x)=sqrt(2)sin(x-pi/4) This is why I got stuck. I will do a few more today.