Question

Verify the identity.

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

Answer 1

Use property...

cot(a+b)=cot a cot b - tan a tan b

a=x b=pi/2

Left side --> cot x+pi/2)=cot x cot (pi/2) - tan x tan (pi/2)

= cot x * 0 - tan x * 1

=0 - tan x

=- tan x

= Right side