decide whether the expression is or is not an identity cot2

decide whether the expression is or is not an identity. cot^2 x/2 = sec x +1 /sec x-1

Solution

cot^2 x/2 = sec x +1 /sec x-1

RHS: sec x +1 /sec x-1

Lets try and make it equal to LHS

sec x +1 /sec x-1 = (1/cosx +1)/( 1/cosx -1)

=( 1+cosx)/( 1-cosx)

Use the trig formulas : cos2y = 2cos^2(y) -1 ; cos2y = 1- 2sin^2(y)

So, = 2cos^2(x/2) /2sin^2(x/2)

= cot^2(x/2)

= LHS

Henec proved that its is a trigonmetric identity