Algebra II Part 2
posted by Karen on .
Verify the identity cot{0pi/2=tan 0

use the identities:
tan(x)=sin(x)/cos(x)
cot(x)=cos(x)/sin(x)
and
sin(π/2)=1, cos(π/2)=0
sin(0)=0, cos(0)=1 
I think she means θ when using 0
I'll use x to avoid copy/paste of special characters.
one way:
recall the definition of cofunctions: function of complementary angle. So,
cos(x) = sin(pi/2  x)
cot(x) = tan(pi/2 x)
so, cot(xpi/2) = cot(pi/2  x) = tan(x)
or, use cot addition formula:
cot(xpi/2) = (1+cotx cot pi/2)/(cot pi/2  cot x) = (1+0)/(0cotx) = 1/cotx = tanx 
Thanks Steve, good thought!