Question

Verify the identity. cot (x-pi/2)= -tan x

Answer 1

Working on the left hand side, you get:
\[\frac{ 1 }{ \tan (x-\frac{ \Pi }{ 2 }) }\]
After that, follow the property that:\[\tan(A-B)=\frac{ tanA-tanB }{ 1+tanAtanB }\]
Giving us:
\[\frac{ 1 }{ \frac{ tanx-\tan \frac{ \Pi }{ 2 } }{ 1+tanxtan \frac{ \Pi }{ 2 } } }=\frac{ 1+tanxtan \frac{ \Pi }{ 2 } }{ tanx-\tan \frac{ \Pi }{ 2 } }\]

Answer 2

From here, we can use the calculator to find tan pi/2 .

Answer 3

or you could convert cot into cos/sin

and directly use,
cos (x-pi/2) = sin x
sin (x-pi/2) = -cos x