Question

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

Answer 1

\[\cot \left( x-\frac{ \pi }{ 2 } \right)= -\tan x\]

Answer 2

@shaik0124 Can you help me?

Answer 3

Use the definition of cotangent, which is cot(x) = 1/tan(x) = cos(x)/sin(x).\[\Large \frac{\cos(x-\frac{\pi}{2})}{\sin(x-\frac{\pi}{2})}=-\tan(x)\]When you subtract pi/2 in the argument of sine or cosine, simply move the graph to the right by pi/2 to see what you get.
So the top is sin(x) and bottom is -cos(x).\[\Large -\frac{\sin(x)}{\cos(x)}=-\tan(x)\]sin(x)/cos(x) is tan(x) so identity is verified.\[\Large-\tan(x)=-\tan(x)\]