## gjhfdfg 3 years ago Verify the identity. cot ( theta - pi / 2 ) = - tan theta

1. Zekarias

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

2. Kashan

cot ( theta - pi / 2 )= cos ( theta - pi / 2 ) / sin ( theta - pi / 2 ) cos ( theta - pi / 2 )= cos(theta) cos (pi/2) + sin(theta) sin (pi/2) = cos(theta) (0) + sin(theta) (1) = sin(theta) sin ( theta - pi / 2 )= sin(theta) cos(pi/2) - cos(theta) sin(pi/2) = sin(theta) (0) - cos(theta) (1) = -cos(theta) so you get, cot ( theta - pi / 2 )= sin(theta) / -cos(theta) cot ( theta - pi / 2 )= -tan(theta)

3. Zekarias

For any CO - trigonometric functions m(x) and co-m(x), this property is always true.$m(x)=co -m(\pi/2-x)=co -m(x-\pi/2).....or ..vise..versa----if ..m(x)..is ..even$$m(x)=co -m(\pi/2-x)=-co -m(x-\pi/2).....or ..vise..versa----if ..m(x)..is ..odd$

4. Kashan

got it now..??

5. Zekarias

The first one is for even function and the second one for odd.

6. Kashan

@gjhfdfg ????

7. gjhfdfg

I think so.?

8. gjhfdfg

Alright I get it thank you.!