Question

Prove the following trigonometric identities.

`sin^2 A + 1/(1 + tan^2 A) = 1`

Answer 1

^{We know that,}

`sin^2 A + cos^2 A = 1`

`sec^2 A - tan^2A = 1`

So

`sin^2 A + 1/(1 + tan^2 A) = sin^2 A + 1/sec^2 A`

`= sin^2 A + (1/sec A)^2`

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

`= sin^2 A + cos^2 A`

= 1