Show that `((1+tan ^(2) A) /(1+cot ^(2) A ) ) =((1+ tan )/( 1-cot A ))^(2)= tan ^(2) A `

Show that (1- tan ^(2) A ) /( cot ^(2) A-1) =tan ^(2) A

( 2tan 30 ^(@) )/( 1+tan ^(2) 45^(@) ) =

(1+tan^(2)theta)/(1+cot^(2)theta)=

cot^(2) x + tan^(2) x

Prove that cos2A=(1-tan^2 A)/(1+tan^2 A)

Show that tan(45^(@) + A) = (1 + tan A)/(1 - tan A)

Prove that (1 + 1/(tan^2A)) (1 + 1/(cot^2A)) = 1/(sin^2 A - sin^4 A )

Prove that (1 + tan 1^(@)) (1 + tan 2^(@)) (1 + tan 3^(@)) …. (1 + tan 44^(@)) is multiple of 4.

Prove that (1+ tan 1^@ ) (1+ tan 2^@ )...(1+ tan 45º )= 2^23