Question

`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.

Options

• sec² A

• - 1

• cot² A

• tan² A

Answer 1

`(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"`