Verify the identity- tan (x-(3pi/2))=-cotx PLEASE ANSWER QUICKLY. I have a test tomorrow!

To verify tan (x-3pi/2) = -cotx.

Solution:

Consider the left side:

Tan (x-3pi/2) =  Tan (x-3pi +2pi) as tan function is 2pi periodic.

=tan(x+pi/2)

= - tan (supplementary angle of x+Pi/2)

= -tan (pi/2-x)

=-cotx = RHS,  as in triangle ABC with B as triangle, and A as x+pi/2, and C as pi/2 - x, tanA = cotB. Or Tan (x+pi) = cot(pi-x).