Question

How do you prove `1 / (1-sin^2 x) =1+tan^2 x`?

Answer 1

As proved below.

Explanation:

`L H S = 1 / (1 - sin^2 x)`

`=> 1 / cos^2 x`, `"using identity " cos^2x + sin^2x = 1`

`=> sec^2 x`, as `cos x = 1 / sec x`

`=> 1 + tan^2 x` `"using identity " 1 + tan^2x = sec^2x`

`hence = R H S`