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

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

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+1 vote
by (5.9k points)
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Best answer

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

LHS = \(\frac{sec^2A}{cosec^2A} \)(1 + tan2A = sec2A, 1 + cot2A = cosec2A)

LHS = \(​​\frac{sin^2A}{cos^2A} \)

LHS = \(tan^2A\) = RHS

Hence, proved

0 votes
by (130 points)
1+tan²A/1+cot²A
=sec²A/cosec²A
=1/cos²A x 1/cosec²A
=1/cos²A x sin²A
= sin²A/cos²A
=tan²A
Hence proved 

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