Prove the identity (2*cos 2t / sin 2t) - 2*sin^2t = cot t + 1

We have to prove that (2*cos 2t / sin 2t) - 2*(sin t)^2 =
cot t + 1

If this is an identity it should be valid for all
values of x for which cos 2t, sin 2t, sin t and cot t are
valid.

t = 30 degrees is one such
value

(2*cos 2t / sin 2t) - 2*(sin t)^2 = 2* cos 60 / sin
60 - 2* (sin 60)^2

=> 2*2*0.5/sqrt 3 - 2*0.5^2 =
2/sqrt 3 - 0.5

cot 30 + 1 = 3 + 1 = sqrt 3 +
1

As sqrt 3 + 1 is not equal to 2/sqrt 3 - 0.5, the given
expression is not an identity.

We can write the left hand
side as:

(2*cos 2t / sin 2t) - 2*(sin
t)^2

=>2*[(cos t)^2 - (sin t)^2]/2*sin t * cos t -
2*(sin t)^2

=>(cos t/sin t - sin t / cos t - 2*(sin
t)^2

=> cot t - tan t - 2*(sin
t)^2

The given expression is not an
identity.