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Question
`(1+tan^2A)/(1+cot^2A)` = ______.
Options
sec2 A
−1
cot2 A
tan2 A
Solution
`(1+tan^2A)/(1+cot^2A)` = tan2 A.
Explanation:
`(1+tan^2A)/(1+cot^2A) = (1+(sin^2A)/cos^2A)/(1+(cos^2A)/(sin^2A))`
= `((cos^2A + sin^2A)/cos^2A)/((sin^2A + cos^2A)/sin^2A)`
= `(1/cos^2A)/(1/sin^2A)`
= `(sin^2A)/cos^2A`
= `tan^2A`
Hence, alternative tan2 A is correct.
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