Answer to Question #22300 in Trigonometry for katie

Question

prove that cotx+tanx=secx+cscx is equal

Answer 1

cotx+tanx=secx+cscx
we know that
cot(x)=cos(x)/sin(x)
tan(x)=sin(x)/cos(x)
sec(x)=1/cos(x)
csc(x)=1/sin(x)
so we need to show thatcos(x)/sin(x)+sin(x)/cos(x)=1/cos(x)+1/sin(x)
we can multiple both parts sin(x)cos(x):
cos^2(x)+sin^2(x)=sin(x)+cos(x)
1=sin(x)+cos(x)
1=(sin(x)+cos(x))^2
1=1+2sin(x)cos(x)
sin(x)cos(x)=0
but for such x doesn't exist tan(x) or cot(x) so thisequality cant take place cotx+tanx=secx+cscx