Posted by **Karen** on Saturday, May 18, 2013 at 9:01pm.

Verify the identity cot{0-pi/2=-tan 0

- Algebra II Part 2 -
**MathMate**, Saturday, May 18, 2013 at 10:49pm
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

- Algebra II Part 2 -
**Steve**, Sunday, May 19, 2013 at 5:58am
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 co-functions: function of complementary angle. So,

cos(x) = sin(pi/2 - x)

cot(x) = tan(pi/2 -x)

so, cot(x-pi/2) = -cot(pi/2 - x) = -tan(x)

or, use cot addition formula:

cot(x-pi/2) = (1+cotx cot pi/2)/(cot pi/2 - cot x) = (1+0)/(0-cotx) = 1/-cotx = -tanx

- Algebra II Part 2 -
**MathMate**, Sunday, May 19, 2013 at 7:37am
Thanks Steve, good thought!

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