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Question
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Options
sec2 A
−1
cot2 A
tan2 A
Solution
Given:
`(1+tan^2 A)/(1+cot^2 A)`
`= (1+sin^2 A/cos^2 A)/(1+cos^2/sin^2A)`
`=(cos^2 A+sin^2 A/cos^2 A)/(sin^2 A+cos^2 A/sin^2A)`
`=(1/cos^2 A)/(1/sin^2A)`
`=sin^2 A/cos^2 A`
`= tan^2 A`
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