Question

\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to

पर्याय

•  sec² A

• −1

•  cot² A

•  tan² A

Answer 1

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`