Derivative of sqrt(tanx+ sqrt(tanx + sqrt(tanx +....)))

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In this video, i differentiate sqrt(tanx+ sqrt(tanx + sqrt(tanx +....))) using a simple substitution technique
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I solved by sridhar acharya from there. And then got the answer. But too long. Your solution was nice.

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5:00 why did you omit the -sqrt(tanx + 1/4) solution when taking square root on both sides? Can u pls explain

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