Question

Prove that : tan^2x/1+tan^2x+cot^2x/1+cot^2x=1​

Answer 1

tan²x/1+tan²x + cot²x/1+cot²x =  1

Cross Multiplying,

tan²x(1+cot²x) + cot²x(1+tan²x) \ (1+tan²x)(1+cot²x) = 1

⇒ tan²x + cot²x + tan²x + cot²x / 1 + tan²x + cot²x + tan²xcot²x = 1

[ tan²x + cot²x = 2 ]   [ tan²xcot²x = 1 ]

⇒ (2+2) / (1+1+1+1) = 1

⇒ 4 / 4 = 1

⇒ 1 =  1

LHS = RHS..

Hence Proved !!