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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x: $fraction numerator 1 minus cos space straight x over denominator sin space straight x end fraction$

Solution

Let space space space space straight y equals fraction numerator 1 minus cos space straight x over denominator sin space straight x end fraction equals fraction numerator 2 sin squared over denominator 2 sin begin display style straight x over 2 end style cos straight x over 2 end fraction equals tan straight x over 2 therefore space dy over dx equals 1 half sec squared straight x over 2

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