1+tanx/1-tanx = sec^2 x + 2tanx/2-sec^2 x

Take this expression:



The expression above is only well-defined (it's computable) where



Also, in order to get to the right side of the identity, we must assume another restriction for x:



Notice that (ii) includes (i) as a particular case of itself.

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Now, let's see what happens with this expression:







which is what had to be shown.

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Note: This identity is only valid where



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I hope it helps. :-)

Tags: proof prove trigonometric identity tangent tan secant sec restriction

Ibelieve the answer is c