Question

tan square A / 1+ tan square A + cot square A /1+ cot square A = 1 ...... solve this

Answer 1

this is the right answer bro..

Answer 2

$LHS = \frac{tan^{2} A}{1 + tan^{2}A} + \frac{cot^{2} A}{ 1 + cot^{2} A}$

$= \frac{tan^{2} A}{sec^{2}A} + \frac{cot^{2} A}{ cosec^{2} A}$

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By Trigonometric Identities :

1. 1 + tan²A = sec²A
2. 1 + cot²A = cosec²A
3. sin² A + cos² A = 1

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$=\frac{\frac{sin^{2} A}{cos^{2} A}}{ \frac{1}{cos^{2} A } }+ \frac{\frac{cos^{2} A}{sin^{2} A}}{ \frac{1}{sin^{2} A } }$

$= sin^{2} A + cos^{2} A \\= 1 \\= RHS$

$Hence \:Proved$

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