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Question
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
Options
sec2 A
- 1
cot2 A
tan2 A
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Solution
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to tan2 A.
Explanation:
`(1 + tan^2 "A")/(1 + cot^2 "A") = (1 + (sin^2 "A")/(cos^2 "A"))/(1 + (cos^2 "A")/(sin^2 "A")`
= `((cos^2 "A" + sin^2 "A")/(cos^2 "A"))/((sin^2 "A" + cos^2 "A")/(sin^2 "A")) = (1/cos^2 "A")/(1/sin^2 "A")`
= `sin^2 "A"/cos^2 "A" = tan^2 "A"`
∴ `(1 + tan^2 "A")/(1 + cot^2 "A") = tan^2 "A"`
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