Question

Prove that (1+tan²A)/(1+cot²A) = tan²A

Answer 1

(1+tan2A)/(1+cot2A) =tan2A
L.H.S.
(1+tan2A) = sec2A = (1/cos2A)
(1+cot2A) = cosec2A = (1/sin2A)
(1/cos2A) / (1/sin2A) =1/cos2A×sin2A =sin2A/cos2A =tan2A
L.H.S. =R.H.S
( NOTE : 2 MEANS SQUARE OR POWER 2)

Answer 2

Answer:

L.H.S.=1+Tan²A/1+cot²A

=sec²A/cosec²A

=1/cos²A/1/Sin²A

=Sin²A/cos²A

=Tan²A

=R.H.S.