Question

Verify the following identity:
cot(x - pi/2)= -tanx

Answer 1

lets consider a triangle

find tan a and cot b

Answer 2

Thats easy...\[\cot (x-y)=cotx*coty+1/(coty-cotx)\]

Answer 3

put y=pi/2

Answer 4

we get,\[\cot(x-\pi/2)=cotx (cotpi/2)+1/(\cot \pi/2-cotx)\]

Answer 5

this gives answer 1/-cotx=-tanx