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Let f(x)= cosec 2x + cosec^(2)2 x+ cose...

Let `f(x)= cosec 2x + cosec^(2)2 x+ cosec^(2)3 x+........+ cosec^(2)n ,x in (0,pi/2) and g(x)=f(x)+cot 2^n x` . If `H(x)={ [(cosx)^(g(x))+(sec)^(cosecx), if x lt 0], [ p, if x=0] ,[ (e^x+e^(-x)-2cosx)/(x sin x), If x lt 0]}` .Find the value of p, if possible to make the function `H(x)` continuous at `x = 0`.

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