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

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Answer 1 · 2018-03-21T04:10:17

As proved below.

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

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

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

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

$hence = R H S$

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