Question

`(1 + tan^2A)/(1 + cot^2 A)` equals to ______.

विकल्प

• tan² A

• –1

• – tan² A

• cot² A

Answer 1

`(1 + tan^2A)/(1 + cot^2 A)` equals to tan² A.

Explanation:

Substitute the identities into the expression:

`(1 + tan^2A)/(1 + cot^2 A) = (sec^2 A)/("cosec"^2 A)`

Using the definitions of secant and cosecant:

`sec^2 A = 1/(cos^2 A)` and `"cosec"^2 A = 1/(sin^2 A)`

 Therefore, `(sec^2 A)/("cosec"^2 A) = (1/(cos^2 A))/(1/(sin^2 A))`

= `1/(cos^2 A) xx (sin^2 A)/1`

= `(sin^2 A)/(cos^2 A)`

`(sin^2 A)/(cos^2 A) = tan^2 A`

The expression equals tan² A.